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JOURNALS // Diskretnaya Matematika // Archive

Diskr. Mat., 1998 Volume 10, Issue 2, Pages 3–29 (Mi dm424)

This article is cited in 15 papers

Recursive MDS-codes and recursively differentiable quasigroups

S. González, E. Couselo, V. T. Markov, A. A. Nechaev


Abstract: A code of length $n$ over an alphabet of $q\geq 2$ elements is called a full $k$-recursive code if it consists of all segments of length $n$ of a recurring sequence that satisfies some fixed (nonlinear in general) recursivity law $f(x_1,\ldots,x_k)$ of order $k\leq n$. Let $n^r(k,q)$ be the maximal number $n$ such that there exists such a code with distance $n-k+1$ (MDS-code). The condition $n^r(k, q)\geq n$ means that the function $f$ together with its $n-k-1$ sequential recursive derivatives forms an orthogonal system of $k$-quasigroups. We prove that if $q\notin\{2,6,14,18,26,42\}$, then $n^r(2,q)\geq 4$. The proof is reduced to constructing some special pairs of orthogonal Latin squares.

UDC: 519.7

Received: 10.03.1998

DOI: 10.4213/dm424


 English version:
Discrete Mathematics and Applications, 1998, 8:3, 217–245

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