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Algorithm 1059: LinCodeWeightInv—Library for Computing the Weight Distribution of Linear Codes over Finite Fields.

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Titel: Algorithm 1059: LinCodeWeightInv—Library for Computing the Weight Distribution of Linear Codes over Finite Fields.
Autoren: PASHINSKA-GADZHEVA, MARIA1 mariqpashinska@math.bas.bg, BOUYUKLIEV, ILIYA2 iliyab@math.bas.bg
Quelle: ACM Transactions on Mathematical Software. Dec2025, Vol. 51 Issue 4, p1-22. 22p.
Schlagwörter: *LINEAR codes, *FINITE fields, *INSTRUCTION set architecture, *BENCHMARK problems (Computer science), *MATHEMATICAL optimization, *MATHEMATICAL notation
Abstract: We present the Linear Codes Weight Invariant Library (LinCodeWeightInv) for optimized computing of the weight distribution and other weight characteristics of a random linear code (minimum distance, number of codewords with a given weight, etc.). The presented library is developed for linear codes over finite fields with up to 64 elements. We use two main methods for optimizations—efficient algorithms for generating the codewords and integration of extended vector registers with SSE4.1, AVX2, and AVX512 instruction sets for x86 architectures and NEON instructions set for ARM. The LinCodeWeightInv is compared to other software systems for linear codes over finite fields. Comparing our library to the Magma software, we get between 1.3 and 4 times faster execution times for \(\mathbb{F}_{2}\) and \(\mathbb{F}_{5}\) and up to 49 depending on the field and the code length. Comparing the LinCodeWeightInv library to the open source software GAP, we observe a reduction in computation time by factors between 5 and 7 for \(\mathbb{F}_{2}\). For other finite fields, we observe more than 100 times faster execution times. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:We present the Linear Codes Weight Invariant Library (LinCodeWeightInv) for optimized computing of the weight distribution and other weight characteristics of a random linear code (minimum distance, number of codewords with a given weight, etc.). The presented library is developed for linear codes over finite fields with up to 64 elements. We use two main methods for optimizations—efficient algorithms for generating the codewords and integration of extended vector registers with SSE4.1, AVX2, and AVX512 instruction sets for x86 architectures and NEON instructions set for ARM. The LinCodeWeightInv is compared to other software systems for linear codes over finite fields. Comparing our library to the Magma software, we get between 1.3 and 4 times faster execution times for \(\mathbb{F}_{2}\) and \(\mathbb{F}_{5}\) and up to 49 depending on the field and the code length. Comparing the LinCodeWeightInv library to the open source software GAP, we observe a reduction in computation time by factors between 5 and 7 for \(\mathbb{F}_{2}\). For other finite fields, we observe more than 100 times faster execution times. [ABSTRACT FROM AUTHOR]
ISSN:00983500
DOI:10.1145/3777479