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
Lexicographic Order and Linearity
Designs, Codes and Cryptography
Error-Correcting Codes over an Alphabet of Four Elements
Designs, Codes and Cryptography
CG '00 Revised Papers from the Second International Conference on Computers and Games
Greedy loop transversal codes for correcting error bursts
Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
Complexity, appeal and challenges of combinatorial games
Theoretical Computer Science - Algorithmic combinatorial game theory
A framework of greedy methods for constructing interaction test suites
Proceedings of the 27th international conference on Software engineering
On the Construction of Linear q-ary Lexicodes
Designs, Codes and Cryptography
Bounds on Codes Derived by Counting Components in Varshamov Graphs
Designs, Codes and Cryptography
Heuristic algorithms for constructing binary constant weight codes
IEEE Transactions on Information Theory
Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams
IEEE Transactions on Information Theory
A comparison of evolutionary algorithms for finding optimal error-correcting codes
CI '07 Proceedings of the Third IASTED International Conference on Computational Intelligence
A selection of divisible lexicographic codes
International Journal of Information and Coding Theory
Evolutionary approaches to the generation of optimal error correcting codes
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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Lexicographic codes, or lexicodes, are defined by various versions of the greedy algorithm. The theory of these codes is closely related to the theory of certain impartial games, which leads to a number of surprising properties. For example, lexicodes over an alphabet of sizeB=2^{a}are closed under addition, while ifB = 2^{2^{a}}the lexicodes are closed under multiplication by scalars, where addition and multiplication are in the nim sense explained in the text. Hamming codes and the binary Golay codes are lexieodes. Remarkably simple constructions are given for the Steiner systemsS(5,6,12)andS(5,8,24). Several record-breaking constant weight codes are also constructed.