Computer classification of linear codes

Abstract

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.

18 pages, 9 tables; this paper is a merge and extension of arXiv:1907.10363 and arXiv:1912.09357

References in corpus (2)

• Projective divisible binary codes
• The lengths of projective triply-even binary codes

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• Computer classification of linear codes based on lattice point enumeration and integer linear programming
• Lengths of divisible codes -- the missing cases