Optimum commutative group codes
| Autor: | Sueli I. R. Costa, João E. Strapasson, Rogério Monteiro de Siqueira, Cristiano Torezzan |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics Hermite polynomials Information Theory (cs.IT) Computer Science - Information Theory Applied Mathematics Structure (category theory) Group Theory (math.GR) Linear code Hermite normal form Computer Science Applications Factorization Group code FOS: Mathematics Order (group theory) Abelian group Mathematics - Group Theory Mathematics |
| Zdroj: | Designs, Codes and Cryptography. 74:379-394 |
| ISSN: | 1573-7586 0925-1022 |
| Popis: | A method for finding an optimum $$n$$ n -dimensional commutative group code of a given order $$M$$ M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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