Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/⟨u2+1⟩

초록

We find a building-up type construction method for self-orthogonal codes over Z(4) arising from the chain ring Z(4)[u]/< u(2) + 1 >. Our construction produces self-orthogonal codes over Z(4) with increased lengths and free ranks from given self-orthogonal codes over Z(4) with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over Z(4) with generator matrix subject to certain conditions can be obtained from our construction. Employing our construction method, we obtain at least 125 new self-orthogonal codes over Z(4) up to equivalence; among them, there are 35 self-orthogonal codes which are distance-optimal. Furthermore, we have eight self-orthogonal codes, which are distance-optimal among all linear codes over Z(4) with the same type. As a method, we use additive codes over the finite ring Z(4)[u]/< u(2) + 1 > with generator matrices G satisfying GGT = O, and we use a new Gray map from Z(4)[u]/< u(2) + 1 > to Z(4)(3) as well. (C) 2021 Elsevier Inc. All rights reserved.

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