A Recursive Construction for Projective Reed-Muller Codes

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2024-10-21 DOI:10.1109/TIT.2024.3483998

Rodrigo San-José

引用次数: 0

Abstract

We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller codes for some particular degrees that give codes with good parameters. Moreover, from this recursive construction we derive a lower bound for the generalized Hamming weights of projective Reed-Muller codes which is sharp in most of the cases we have checked.

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.