New quantum codes from constacyclic codes over finite chain rings

2024/08/28 by Tang, Yongsheng, Yao, Ting, Xu, Heqian +1
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2408.15558

Abstract

Let R be the finite chain ring \mathbbF_p^2m+u\mathbbF_p^2m, where \mathbbF_p^2m is the finite field with p^2m elements, p is a prime, m is a non-negative integer and u²=0. In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over \mathbbF_2^2m+u\mathbbF_2^2m into the Hermitian self-orthogonal property of linear codes over \mathbbF_2^2m. Applying the Hermitian construction, a new class of 2^m-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over \mathbbF_2^2m+u\mathbbF_2^2m. We secondly define another class of maps, which changes the Hermitian self-orthogonal property of linear codes over R into the trace self-orthogonal property of linear codes over \mathbbF_p^2m. Using the Symplectic construction, a new class of p^m-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over R.

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