Computer classification of linear codes

We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements. We validate a correct implementation of the algorithms with known classification results from the literature, which we partially extend to larger ranges of parameters.Comment: 18 pages, 9 tables; this paper is a merge and extension of arXiv:1907.10363 and arXiv:1912.0935

An Extension of the Brouwer–Zimmermann Algorithm for Calculating the MinimumWeight of a Linear Code

A modification of the Brouwer–Zimmermann algorithm for calculating the minimum weight of a linear code over a finite field is presented. The aim was to reduce the number of codewords for consideration. The reduction is significant in cases where the length of a code is not divisible by its dimensions. The proposed algorithm can also be used to find all codewords of weight less than a given constant. The algorithm is implemented in the software package QextNewEdition

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Използване на AVX инструкции за оптимизация на алгоритми за теглови характеристики на линеен двоичен код

We present methods of using Advanced Vector Extensions (AVX, AVX2, AVX512) for calculation of weight characteristics of binary linear codes. Some experimental results for different lengths and dimensions are presented.The research of Maria Pashinska was supported, in part, by National program "Young scientists and postdoctoral students" РМС №577 от 17.08.2018. The research of Iliya Bouyukliev was supported, in part, by the Bulgarian Ministry of Education and Science by Grant No. DO1-221/03.12.2018 for NCHDC, a part of the Bulgarian National Roadmap on RIs