Self-orthogonal designs and extremal doubly even codes
Journal of Combinatorial Theory Series A
A K-nearest neighbor-based method for the restoration of damaged images
Pattern Recognition
Designs, Codes and Cryptography
Rooted Trees Searching for Cocyclic Hadamard Matrices over D4t
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A heuristic procedure with guided reproduction for constructing cocyclic Hadamard matrices
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
ACS searching for D4t-Hadamard matrices
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
A genetic algorithm for cocyclic hadamard matrices
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Calculating cocyclic hadamard matrices in mathematica: exhaustive and heuristic searches
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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From past literature it is evident that the search for self-dual codes has been hampered by the computational difficulty of generating the Hadamard matrices required. The use of the cocyclic construction of Hadamard matrices has permitted substantial cut-downs in the search time, but the search space still grows exponentially. Here we look at an adaptation of image-processing techniques for the restoration of damaged images for the purpose of sampling the search space systematically. The performance of this approach is evaluated for Hadamard matrices of small orders, where a full search is possible.The dihedral cocyclic Hadamard matrices obtained by this technique are used in the search for self-dual codes of length 40, 56 and 72. In addition to the extremal doubly-even [56,28,12] code, and two singly-even [56,28,10] codes, we found a large collection of codes with only one codeword of minimum length.