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New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X
Abstract
We present linear codes with parameters [88,8,64] and [90,8,65] over GF(7), [98,7,75] and [97,8,72] over GF(8), and [44,7,31] over GF(9). Each has a minimum distance one larger than the lower bound listed in Grassl's tables of best known linear codes; codes with parameters [89,8,64] over GF(7) and [96,8,71], [95,8,70], [94,8,69] over GF(8) follow. Four of the five codes are obtained from a quasi-cyclic code and a vector that is constant on each block, by Construction X with a repetition code. The remaining one, the [90,8,65] code, is obtained from the first by appending two coordinates. The parameters and all weight counts were obtained by exhaustive enumeration, and a short program that repeats these computations is included.
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BibTeX
@misc{cochinescu2026linear,
title = {{New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X}},
author = {Sebastian Cochinescu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.14433},
eprint = {2611.14433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.14433},
}
RIS
TY - UNPB
TI - New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X
AU - Sebastian Cochinescu
PY - 2026
DA - 2026/11/10
PB - arXiv
DO - 10.48550/arxiv.2611.14433
UR - https://arxiv.org/abs/2611.14433
AB - We present linear codes with parameters [88,8,64] and [90,8,65] over GF(7), [98,7,75] and [97,8,72] over GF(8), and [44,7,31] over GF(9). Each has a minimum distance one larger than the lower bound listed in Grassl's tables of best known linear codes; codes with parameters [89,8,64] over GF(7) and [96,8,71], [95,8,70], [94,8,69] over GF(8) follow. Four of the five codes are obtained from a quasi-cyclic code and a vector that is constant on each block, by Construction X with a repetition code. The remaining one, the [90,8,65] code, is obtained from the first by appending two coordinates. The parameters and all weight counts were obtained by exhaustive enumeration, and a short program that repeats these computations is included.
ER -