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Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

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Show simple item record Derka, Martin 2012-09-18T15:01:49Z 2012-09-18T15:01:49Z 2012-09-18
dc.description.abstract Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map. en_US
dc.language.iso eng en_US
dc.publisher Brock University en_US
dc.subject Error-correcting codes en_US
dc.subject Type II codes en_US
dc.subject Automorphism group en_US
dc.subject Permutation en_US
dc.title Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes en_US
dc.type Electronic Thesis or Dissertation en_US M.Sc. Computer Science en_US Masters en_US
dc.contributor.department Department of Computer Science en_US Faculty of Mathematics and Science en_US

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