The minimum weight of the code of intersecting lines in \rm PG(3,q)

2024/03/12 by Sam Adriaensen, Adriaensen, Sam, Robin Simoens +3 · 1 citation
Computer Science · Engineering · #05B25 #51A50 #51E21 #94B05 #Advanced Wireless Communication Techniques #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2403.07451

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterise the minimum weight codewords of the p-ary linear code of intersecting lines in \rm 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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