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Parameters of recursive MDS-codes. (English. Russian original) Zbl 1020.94020
Discrete Math. Appl. 10, No. 5, 433-453 (2000); translation from Diskret. Mat. 12, No. 4, 3-24 (2000).
Given an alphabet \(\Omega\), a full \(m\)-recursive code over \(\Omega\) consists of segments of recurring sequences that satisfy a recursivity law \(f:\Omega^m \rightarrow \Omega\). Full \(m\)-recursive codes are related to orthogonal systems of \(m\)-quasigroups. An MDS code is a code meeting the Singleton bound, i.e. an \([n,k,n-k+1]\) code. The authors give conditions for which recursive MDS codes exist. They build on results from their previous paper showing that the largest length for which a full \(m\)-recursive code over an alphabet of size \(q\) exists is greater than or equal to \(q+1\) for primary \(q\) with \(1\leq m \leq q\) and is \(2^t+2\) when \(m=2^t-1\), \(q=2^t\) for \(t=2,3,4.\)

MSC:
94B05 Linear codes (general theory)
20N05 Loops, quasigroups
05B15 Orthogonal arrays, Latin squares, Room squares
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