Linear Codes from Projective Varieties: A Survey

Abstract

Linear codes can be constructed from classical algebraic varieties or from appropriate subsets of finite geometry by considering projective systems arising from their rational points. This geometric point of view allows to look for linear codes by choosing suitable sets to get immediately length, minimum distance, and spectrum (cf. Lemma 1, Propositions 5, 9, 12, 13, 17). In some cases, it is also possible to build a PD-set or an antiblocking decoding (cf. Propositions 3, 4, 14, Examples of Section 5).