March 3, 2026Open Access

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

Key Points

The minimum weight of codewords for even q equals q³ + q² + q + 1, while for odd q it equals q³ + 2q² + q + 1.
This work highlights the distinct weight characteristics of codewords based on whether q is even or odd.
Characterization of the second minimum weight codewords is provided for cases when q is even, expanding our understanding of code structure.
Focus on p-ary linear codes in PG(3,q) enhances the existing knowledge of finite projective spaces and their applications.

Abstract

We characterise the minimum weight codewords of the p-ary linear code of intersecting lines in PG (3, q), q = pʰ, 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.

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

Key Points

Abstract

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