2022/08/29 by Li, Yang, Su, Yunfei, Zhu, Shixin +2
#12E10 #15B05 #94B05 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2208.13389
Let q=ph be a prime power and e be an integer with 0≤ e≤ h-1. e-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes (e=0) and Hermitian self-orthogonal codes (e=(h)/(2) and h is even). In this paper, we propose two general methods to construct e-Galois self-orthogonal (extended) generalized Reed-Solomon (GRS) codes. As a consequence, eight new classes of e-Galois self-orthogonal (extended) GRS codes with odd q and 2e| h are obtained. Based on the Galois dual of a code, we also study its punctured and shortened codes. As applications, new e'-Galois self-orthogonal maximum distance separable (MDS) codes for all possible e' satisfying 0≤ e'≤ h-1, new e-Galois self-orthogonal MDS codes via the shortened codes, and new MDS codes with prescribed dimensional e-Galois hull via the punctured codes are derived. Moreover, some new √(q)-ary quantum MDS codes with lengths greater than √(q)+1 and minimum distances greater than (√(q))/(2)+1 are obtained.