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TheGF(p)-dimension of the codes generated by the classical point-line geometries overGF(p)

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Abstract

In this note we develop a combinatorial-algebro-geometric approach to give a new self-contained analysis of the structure and dimension of theGF(p)-codes generated by the point-line geometriesAG 1 (n, p) andPG 1 (n, p) of dimensionn overGF(p) as coordinate field. The novelty of this paper is a beautiful representation of these codes as nil-ideals of the modular group algebra\(\mathbb{F}_p [\mathbb{Z}_p )^n ]\), which leads to an easy derivation of the dimension formula.

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Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, Am Fasanengarten 5, 7500, Karlsruhe 1, Germany

    Thomas Beth

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  1. Thomas Beth
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Communicated by D. Jungnickel

Dedicated to Professor Konrad Jacobs, Erlangen, on the occasion of this 65th birthday.

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Beth, T. TheGF(p)-dimension of the codes generated by the classical point-line geometries overGF(p) . Des Codes Crypt 3, 199–207 (1993). https://doi.org/10.1007/BF01388481

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  • DOI: https://doi.org/10.1007/BF01388481

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