Griesmer Bound and Constructions of Linear Codes in $b$-Symbol Metric
Information Theory
2024-01-11 v1 math.IT
Abstract
The -symbol metric is a generalization of the Hamming metric. Linear codes, in the -symbol metric, have been used in the read channel whose outputs consist of consecutive symbols. The Griesmer bound outperforms the Singleton bound for -linear codes in the Hamming metric, when is fixed and the length is large enough. This scenario is also applicable in the -symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the -symbol metric. In this paper, we present the -symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the -symbol Griesmer bound.
Keywords
Cite
@article{arxiv.2401.04941,
title = {Griesmer Bound and Constructions of Linear Codes in $b$-Symbol Metric},
author = {Gaojun Luo and Martianus Frederic Ezerman and Cem Güneri and San Ling and Ferruh Özbudak},
journal= {arXiv preprint arXiv:2401.04941},
year = {2024}
}