New Constant Weight Codes and Packing Numbers
| Autor: | Iliya Bluskov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Applied Mathematics 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences 010201 computation theory & mathematics Mod 0202 electrical engineering electronic engineering information engineering Code (cryptography) Discrete Mathematics and Combinatorics Binary code Constant (mathematics) Mathematics |
| Zdroj: | Electronic Notes in Discrete Mathematics. 65:31-36 |
| ISSN: | 1571-0653 |
| DOI: | 10.1016/j.endm.2018.02.017 |
| Popis: | The constant A ( n , d , w ) is the maximum number of words in an ( n , d , w ) binary code, that is, a code of minimal distance d, with words of length n and weight w. We improve the best known lower bounds on A ( n , d , w ) for three sets of parameters by using optimization; in particular, we show that A ( 29 , 8 , 5 ) ≥ 36 , A ( 30 , 8 , 5 ) ≥ 41 , and A ( 32 , 8 , 5 ) = 44 by explicitly giving the respective codes. The (32, 8, 5) code is optimal and leads to eight more new optimal codes. We show this by improving the known result on the problem of finding the packing number P ( v , 5 , 2 ) for v ≡ 12 (mod 20). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect