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

Research paper by Thomas Beth

Indexed on: 01 Jul '93Published on: 01 Jul '93Published in: Designs, Codes and Cryptography



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 geometriesAG1(n, p) andPG1(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.