منابع مشابه
Skew codes of prescribed distance or rank
In this paper we propose two methods to produce block codes of prescribed rank or distance. Following [4, 5] we work with skew polynomial rings of automorphism type and the codes we investigate are ideals in quotients of this ring. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section. 1 Galois theory of di...
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Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature. In this work, we introduce a linearized version of such codes, called linearized Reed-Solomon codes. We prove that they have maximum sum-rank distance. Such dist...
متن کاملRank equivalent and rank degenerate skew cyclic codes
Two skew cyclic codes can be equivalent for the Hamming metric only if they have the same length, and only the zero code is degenerate. The situation is completely different for the rank metric, where lengths of codes correspond to the number of outgoing links from the source when applying the code on a network. We study rank equivalences between skew cyclic codes of different lengths and, with...
متن کاملOn the roots and minimum rank distance of skew cyclic codes
Skew cyclic codes play the same role as cyclic codes in the theory of errorcorrecting codes for the rank metric. In this paper, we give descriptions of these codes by idempotent generators, root spaces and cyclotomic spaces. We prove that the lattice of skew cyclic codes is anti-isomorphic to the lattice of root spaces and extend the rank-BCH bound on their minimum rank distance to rank-metric ...
متن کاملConstruction of linear codes with prescribed minimum distance
We construct linear codes over finite fields with prescribed minimum distance by selectiong columns of the generator matrix. This selection problem can be formulated as an integer programming problem. In order to reduce the search space we prescribe a group of automorphisms. Then, in many cases the resulting integer programming problem can be solved by lattice point enumeration. With this appro...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2008
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-008-9230-6