AI & ML
New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X
arXiv math.IT0 views
arXiv:2611.14433v1 Announce Type: new 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.
Source：https://arxiv.org/abs/2611.14433PreviousAn Information-Theoretic Perspective on Regulatory T Cell Localization as an IL-2 Interference FilterNextMonitoring One Channel Is Not Communication Control: Causal Evidence for Adaptive Reallocation of Joint Message--Route Codes
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