Bounds for self-dual codes over \(\mathbb{Z}_4\) (Q1570226)

This paper presents new bounds on the minimum Hamming and Lee distances of self-dual codes over \(\mathbb{Z}_4\). For a self-dual code \(C\) of length \(n\), the Hamming weight is bounded by \(H(C) \leq 4[n/24] + f(n \bmod 24)\), for an explicitly given function \(f\). The Lee weight of a code \(C\) is bounded by the simple inequality \(L(C) \leq 2H(C)\), and this is used to obtain the Lee weight bound \(L(C) \leq 8[n/24] + g(n \bmod 24)\), where \(g\) is a function different from \(f\). Over a wide range of lengths, these bounds agree with the linear programming bound. The proof of these bounds relies on bounding the minimum dual distance of a doubly even binary code.