title: Mutually orthogonal binary frequency squares

authors: Britz, Thomas

abstract: A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order n with n/2 zeros and n/2 ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of k-MOFS (n) is a set of k binary frequency squares of order n in which each pair of squares is orthogonal.

A set of k-MOFS (n) must satisfy k≤(n−1)², and any set of MOFS achieving this bound is said to be complete. For any n for which there exists a Hadamard matrix of order n we show that there exists at least 2 ⁿ²/⁴−ᴼ ⁽ⁿˡᵒᵍⁿ ⁾ isomorphism classes of complete sets of MOFS (n). For 2<n≡2(mod 4) we show that there exists a set of 17-MOFS(n) but no complete set of MOFS(n).

A set of k –maxMOFS (n) is a set of k-MOFS(n) that is not contained in any set of (k+1)-MOFS(n). By computer enumeration, we establish that there exists a set of k-maxMOFS(6) if and only if k∈{1,17} or 5≤k≤15. We show that up to isomorphism there is a unique 1-maxMOFS(n) if n≡2(mod4), whereas no 1-maxMOFS(n) exists for n≡0(mod4). We also prove that there exists a set of 5-maxMOFS(n) for each order n≡2(mod4) where n≥6.

text: Mutually orthogonal binary frequency squares A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order n with n/2 zeros and n/2 ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of k-MOFS (n) is a set of k binary frequency squares of order n in which each pair of squares is orthogonal.

A set of k-MOFS (n) must satisfy k≤(n−1)², and any set of MOFS achieving this bound is said to be complete. For any n for which there exists a Hadamard matrix of order n we show that there exists at least 2 ⁿ²/⁴−ᴼ ⁽ⁿˡᵒᵍⁿ ⁾ isomorphism classes of complete sets of MOFS (n). For 2<n≡2(mod 4) we show that there exists a set of 17-MOFS(n) but no complete set of MOFS(n).

A set of k –maxMOFS (n) is a set of k-MOFS(n) that is not contained in any set of (k+1)-MOFS(n). By computer enumeration, we establish that there exists a set of k-maxMOFS(6) if and only if k∈{1,17} or 5≤k≤15. We show that up to isomorphism there is a unique 1-maxMOFS(n) if n≡2(mod4), whereas no 1-maxMOFS(n) exists for n≡0(mod4). We also prove that there exists a set of 5-maxMOFS(n) for each order n≡2(mod4) where n≥6.

year: 2020

title: A woman's reckoning: a feminist analysis of the power of the internationally accepted conception and implementation of the United Nations System of National Accounts

authors: Waring, Marilyn J.

subjects: United Nations System of National Accounts

abstract: The United Nations System of National Accounts (UNSNA) was the formal and global institutionalization of the development of national accounts over a period of several centuries. Each man responsible for the development is historically located within a government in the midst of mercantile, colonial expansionism (civil and colonial wars) or global conflict (World Wars I & II).
While apologists for the pathology now evident in the implementation of the UNSNA describe its conception as an attempt, with limited indicators and blunt tools, to produce the best possible measurement system for a particular short-term historical contingency, the over-riding ideology of power inherent in the conception and implementation of the UNSNA is patriarchy. Given the maintaining this system in place are devastating - both to and for the majority of the human species, and for the eco-system of the planet. 
This thesis establishes the conception of the UNSNA in Western political and economic patriarchal ideology. It exposes, in the narrow terms of the UNSNA, the major flaws of the system, and the passage of 'blame' from one 'profession' to another in locating responsibility for the perpetuation of a chronically impaired system.
Then the thesis examines the nature of 'reproduction' not as 'another form of production', but as the primary exchange, the economic principle before and beyond which no production can exist. The absence of this concept from political economy, even as an extended debate is distinctly patriarchal.
The environment, by way of analogy with women and children, suffers a similar rape, abuse, enslavement, and invisibility in the conception and implementation of the UNSNA. The global resource abuses and the policy consequences of such a treatment are examined in detail.
Various reforms suggested of the UNSNA have been and are being developed. While some would offer the possibility of short-term policy options which would be of some improvement, the problem of pursuing only one indicator, the market dollar, remains. My own experience as a legislator has seen this as a barren basic, and I discuss a variety of options.
Throughout 'A Woman's Reckoning', the approach is one of feminist scholarship, and the theoretical and political base of the thesis are unavoidably those of an enquiring activist.

text: A woman's reckoning: a feminist analysis of the power of the internationally accepted conception and implementation of the United Nations System of National Accounts The United Nations System of National Accounts (UNSNA) was the formal and global institutionalization of the development of national accounts over a period of several centuries. Each man responsible for the development is historically located within a government in the midst of mercantile, colonial expansionism (civil and colonial wars) or global conflict (World Wars I & II).
While apologists for the pathology now evident in the implementation of the UNSNA describe its conception as an attempt, with limited indicators and blunt tools, to produce the best possible measurement system for a particular short-term historical contingency, the over-riding ideology of power inherent in the conception and implementation of the UNSNA is patriarchy. Given the maintaining this system in place are devastating - both to and for the majority of the human species, and for the eco-system of the planet. 
This thesis establishes the conception of the UNSNA in Western political and economic patriarchal ideology. It exposes, in the narrow terms of the UNSNA, the major flaws of the system, and the passage of 'blame' from one 'profession' to another in locating responsibility for the perpetuation of a chronically impaired system.
Then the thesis examines the nature of 'reproduction' not as 'another form of production', but as the primary exchange, the economic principle before and beyond which no production can exist. The absence of this concept from political economy, even as an extended debate is distinctly patriarchal.
The environment, by way of analogy with women and children, suffers a similar rape, abuse, enslavement, and invisibility in the conception and implementation of the UNSNA. The global resource abuses and the policy consequences of such a treatment are examined in detail.
Various reforms suggested of the UNSNA have been and are being developed. While some would offer the possibility of short-term policy options which would be of some improvement, the problem of pursuing only one indicator, the market dollar, remains. My own experience as a legislator has seen this as a barren basic, and I discuss a variety of options.
Throughout 'A Woman's Reckoning', the approach is one of feminist scholarship, and the theoretical and political base of the thesis are unavoidably those of an enquiring activist.

year: 1989

title: Barriers and facilitators to Oranga Tamariki access: Wāhine voices from Te Whakaruruhau

authors: Mcleay, Ana

abstract: This thesis examines how wāhine supported by Te Whakaruruhau Waikato Women’s Refuge experience Oranga Tamariki (OT) in the context of intimate partner violence (IPV), and what barriers and facilitators shape their access to services. Within a Community-Based Participatory Research approach, influenced by Kaupapa Māori and Mana Wahine principles, qualitative data were collected through semi-structured, kanohi ki te kanohi interviews with six wāhine and kaimahi. Reflexive thematic analysis identified seven themes, grouped into two overarching clusters: barriers and facilitators to OT access. Barriers were pervasive and cumulative, encompassing relational harm, negligence, fear and risk, and cultural tokenism. Facilitators - collaborative advocacy, strengths-based practice, and procedural justice - were comparatively rare and often dependent on external supports rather than systemic provision.

Mapping these findings against Te Hā o Whānau, an access framework, revealed that barriers emerged where tikanga manaakitanga, tikanga whakawhanaungatanga, and tikanga rangatiratanga were absent, while facilitators aligned with their enactment. Te Hā o Whānau conceptualises access as a relational and culturally grounded process inseparable from wellbeing, making it both conceptually robust and uniquely suited to Aotearoa. The analysis demonstrates that OT, as currently structured, undermines whānau wellbeing through systemic practices that erode mana, restrict autonomy, and compromise safety. In the immediate term, strengthened collaborative advocacy offers some protection and support, but meaningful change requires systemic transformation.

Future research should examine how Te Hā o Whānau might be further operationalised across different service contexts and explore experiences of wāhine and whānau with OT in a variety of contexts to build a fuller understanding of access and wellbeing in child welfare.

text: Barriers and facilitators to Oranga Tamariki access: Wāhine voices from Te Whakaruruhau This thesis examines how wāhine supported by Te Whakaruruhau Waikato Women’s Refuge experience Oranga Tamariki (OT) in the context of intimate partner violence (IPV), and what barriers and facilitators shape their access to services. Within a Community-Based Participatory Research approach, influenced by Kaupapa Māori and Mana Wahine principles, qualitative data were collected through semi-structured, kanohi ki te kanohi interviews with six wāhine and kaimahi. Reflexive thematic analysis identified seven themes, grouped into two overarching clusters: barriers and facilitators to OT access. Barriers were pervasive and cumulative, encompassing relational harm, negligence, fear and risk, and cultural tokenism. Facilitators - collaborative advocacy, strengths-based practice, and procedural justice - were comparatively rare and often dependent on external supports rather than systemic provision.

Mapping these findings against Te Hā o Whānau, an access framework, revealed that barriers emerged where tikanga manaakitanga, tikanga whakawhanaungatanga, and tikanga rangatiratanga were absent, while facilitators aligned with their enactment. Te Hā o Whānau conceptualises access as a relational and culturally grounded process inseparable from wellbeing, making it both conceptually robust and uniquely suited to Aotearoa. The analysis demonstrates that OT, as currently structured, undermines whānau wellbeing through systemic practices that erode mana, restrict autonomy, and compromise safety. In the immediate term, strengthened collaborative advocacy offers some protection and support, but meaningful change requires systemic transformation.

Future research should examine how Te Hā o Whānau might be further operationalised across different service contexts and explore experiences of wāhine and whānau with OT in a variety of contexts to build a fuller understanding of access and wellbeing in child welfare.

year: 2025