Lexicographic codes: Error-correcting codes from game theory
IEEE Transactions on Information Theory
Discrete Mathematics - Coding Theory
Journal of Combinatorial Theory Series A
Forcing Linearity on Greedy Codes
Designs, Codes and Cryptography - Special issue containing papers presented at the Second Upper Michigan Combinatorics Workshop on Designs, Codes and Geometries
Designs, Codes and Cryptography - Special issue containing papers presented at the Second Upper Michigan Combinatorics Workshop on Designs, Codes and Geometries
Journal of Combinatorial Theory Series A
Lexicographic Order and Linearity
Designs, Codes and Cryptography
Handbook of Coding Theory
Designing lexicographic codes with a given trellis complexity
IEEE Transactions on Information Theory
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Let V be a list of all vectors of GF(q)n, lexicographically ordered with respect to some basis. Algorithms which search list V from top to bottom, any time selecting a codeword which satisfies some criterion, are called greedy algorithms and the resulting set of codewords is called a lexicode. In many cases such a lexicode turns out to be linear. In this paper we present a greedy algorithm for the construction of a large class of linear q-ary lexicodes which generalizes the algorithms of several other papers and puts these into a wider framework. By applying this new method, one can produce linear lexicodes which cannot be constructed by previous algorithms, because the characteristics or the underlying field of the codes do not meet the conditions of those algorithms.