Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

2023/03/29 by Minjia Shi, Shi, Minjia, Shitao Li +5 · 2 citations
Computer Science · Engineering · #94B05 #Advanced Wireless Communication Techniques #Coding theory and cryptography #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2303.16729

openalex publication_date 2023/03/29 · openalex created_date 2023/04/05 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Second, using such a characterization, we determine the exact value of d_so(n,7) except for five special cases and the exact value of d_so(n,8) except for 41 special cases, where d_so(n,k) denotes the largest minimum distance among all binary self-orthogonal [n, k] codes. Currently, the exact value of d_so(n,k) (k ≤ 6) was determined by Shi et al. (2022). In addition, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code.

Cited by

• Shortest self-orthogonal embeddings of binary linear codes
• Constructions of binary self-orthogonal singly-even minimal linear codes violating the Aschikhmin-Barg condition with few weights

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