T. Alderson

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20242026

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5 papers · 1 filter

math.CO2026

Length-Maximal Codes with Given Singleton Defect: Structure and Bounds

Tim Alderson

Let $C$ be an $(n, q^{k}, d)_{q}$ code of integer dimension $k \geq 2$ and Singleton defect $s = n - k + 1 - d$ . Repeated shortening followed by the Plotkin bound gives \[ n\le (s+1)(q+1)+…

math.CO2026

Sets of subspaces with restricted hyperplane intersection numbers

Tim Alderson, Simeon Ball

Let $X$ be a set of $(h - 1)$ -dimensional subspaces of $PG (k h - 1, q)$ with the property that every hyperplane contains at most $t$ elements of $X$ . We prov…

math.CO2025

When Arcs Extend Uniquely: A Higher-Dimensional Generalization of Barlotti's Result

Tim L. Alderson

In this short communication, we generalize a classical result of Barlotti concerning the unique extendability of arcs in the projective plane to higher-dimensional projective space…

math.CO2025

Projective systems and bounds on the length of codes of non-zero defect

Tim L. Alderson, Zhipeng Zhang

We derive bounds on the lengths of linear codes with fixed Singleton defect $s$ , working within the framework of projective systems as advocated by Tsfasman and Vlǎduţ. This geomet…

math.CO2024

Bounds on MLDR Codes Over $Z_{p^{t}}$