A class of 1-generator repeated root quasi-cyclic codes
Let \(q\) be a power of a prime integer \(p, m=p^em_0\) and \(|q|_{m_{0}}\) the order of \(q\) modulo \(m_0\). By use of finite commutative chain ring theory, an algorithm to construct all distinct 1-generator quasi-cyclic codes with a fixed parity check polynomial over a finite field \(F_q\) of length \(mn\) and index \(n\), under the condition that \(\mathrm {gcd}(|q|_{m_0},n)=1\), are given.
1-generator repeated root quasi-cyclic code finite commutative chain ring parity check polynomial group of units 94b05 11t71 11t55 13m05