Extremal and Optimal Codes
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A basic problem in coding theory is to find codes with large minimal distance (Hamming, Lee, or Euclidean distance, as appropriate). In order to decide if a particular code is good, it is necessary to know how good comparable codes could be; that is, for a given length and dimension, what is the optimal minimal distance? For general codes, this question is discussed in many references—see for example [361, Chap. 17], and Chapters 4 (by Brouwer ), 5 (by Levenshtein ), and 6 (by Litsyn ) of The Handbook of Coding Theory . In the present book, of course, we are interested in self-dual codes. As one might imagine, the constraint of self-duality usually leads to stronger bounds.
KeywordsOptimal Code Weight Enumerator Extremal Type Unimodular Lattice Negacyclic Code
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