Najmanjša teža kode presečnih premic v PG(3, q)

We characterise the minimum weight codewords of the p-ary linear code of intersecting lines in PG(3,q), q = p^h, q ≥ 19, p prime, h ≥ 1. If q is even, the minimum weight equals q³ + q² + q + 1. If q is odd, the minimum weight equals q³ + 2q² + q + 1. For q even, we also characterise the codewords of second smallest weight.

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Publication Details

Journal
Repository of the University of Primorsk (University of Primorska)
Published
2025-11-07
Primary Topic
Coding theory and cryptography
Type
article
Field-Weighted Citation Impact
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article

Najmanjša teža kode presečnih premic v PG(3, q)

Sam Adriaensen, Robin Simoens, Leo Storme
Repository of the University of Primorsk (University of Primorska)
Coding theory and cryptography
article

Najmanjša teža kode presečnih premic v PG(3, q)

Sam Adriaensen, Robin Simoens, Leo Storme
article en

Abstract

We characterise the minimum weight codewords of the p-ary linear code of intersecting lines in PG(3,q), q = p^h, q ≥ 19, p prime, h ≥ 1. If q is even, the minimum weight equals q³ + q² + q + 1. If q is odd, the minimum weight equals q³ + 2q² + q + 1. For q even, we also characterise the codewords of second smallest weight.

Repository of the University of Primorsk (University of Primorska)
Openalex Percentile: Top 15%
Coding theory and cryptography
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