Sequences of linear codes where the rate times distance grows rapidly

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For a linear code C of length n with dimension k and minimum distance d, it is desirable that the quantity kd/n is large. Given an arbitrary field F, we introduce a novel, but elementary, construction that produces a recursively defined sequence of F-linear codes (formula presented) with parameters (formula presented) grows quickly in the sense that (formula presented). Another example of quick growth comes from a certain subsequence of Reed-Muller codes. Here the field is F = F2 and kidi/ni is asymptotic to (formula presented).

Original languageEnglish
Pages (from-to)105-113
Number of pages9
JournalJournal of Algebra Combinatorics Discrete Structures and Applications
Issue number2
Publication statusPublished - 10 May 2023


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