A new class of optimal optical orthogonal codes with weight five
A (v, k, 1) optical orthogonal code (OOC), or briefly a (v, k, 1)-OOC, C, is a family of (0, 1) sequences of length v and weight k satisfying the following two properties: 1) Sigma(0less than or equal totless than or equal tov-1)x(t)x(t+i) less than or equal to 1 for any x = (x(0), x(1), ..., x(v-1)) is an element of C and any integer inot equivalent to 0 (mod v); 2) Sigma(0less than or equal totless than or equal tov-1)x(t)y(t+i) less than or equal to 1 for any x = (x(0), x(1), ..., x(v-1)) is an element of C, y = (y(0), y(1), ..., y(v-1)) is an element of C with x not equal y, and any integer i, where the subscripts are reduced modulo v.A (v, k, 1)-OOC is optimal if it contains [(v - 1)/k(k - 1)] codewords. In this note, we establish that there exists an optimal (3(s)5 v, 5, 1)-OOC for any nonnegative integer s whenever v is a product of primes congruent to 1 modulo 4. This improves the known existence results concerning optimal OOCs.
optimal optical orthogonal code (ooc) cyclic packing difference matrix (dm) g-regular