Computer classification of linear codes based on lattice point enumeration

Titelangaben

Kurz, Sascha:
Computer classification of linear codes based on lattice point enumeration.
In: Buzzard, Kevin ; Dickenstein, Alicia ; Eick, Bettina ; Leykin, Anton ; Ren, Yue (Hrsg.): Mathematical Software - ICMS 2024 : 8th International Conference on Mathematical Software, Durham, UK, July 22–25, 2024, Proceedings. - Cham : Springer , 2024 . - S. 97-105 . - (Lecture Notes in Computer Science ; 14749 )
ISBN 978-3-031-64528-0
DOI: https://doi.org/10.1007/978-3-031-64529-7_11

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Abstract

Linear codes related to applications in Galois Geometry often require a certain divisibility of the occurring weights. In this paper we present an algorithmic framework for the classification of linear codes over finite fields with restricted sets of weights. The underlying algorithms are based on lattice point enumeration and integer linear programming. We present new enumeration and non-existence results for projective two-weight codes, divisible codes, and additive GF(4)-codes.