Programs and Dataset for the LCD paper

A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2024-09-03
DOI
https://doi.org/10.1016/j.dam.2018.10.032
Citations
4
Primary Topic
Coding theory and cryptography
Type
article
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article

Programs and Dataset for the LCD paper

4 citations
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
article

Programs and Dataset for the LCD paper

article en
4 citations

Abstract

A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.

Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
DOIOpen Access PDFOpenAlex
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Programs and Dataset for the LCD paper · Zenodo (CERN European Organization for Nuclear Research) (2024) | TGRS Research Map | TGRS