Embedding Linear Codes Into Self-Orthogonal Codes and Their Optimal Minimum Distances
- 주제(키워드) 도움말 Binary linear code , self-orthogonal code , optimal code
- 발행기관 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- 발행년도 2021
- 총서유형 Journal
- 본문언어 영어
초록/요약 도움말
We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an algorithmic method to embed a given binary k-dimensional linear code C ( k = 3, 4) into a self-orthogonal code of the shortest length which has the same dimension k and minimum distance d' >= d(C). For k > 4, we suggest a recursive method to embed a k-dimensional linear code to a self-orthogonal code. We also give new explicit formulas for the minimum distances of optimal self-orthogonal codes for any length n with dimension 4 and any length n not equal 6, 13, 14, 21, 22, 28, 29 (mod 31) with dimension 5.
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