Linear size optimal q-ary constant-weight codes and constant-composition codes
An optimal constant-composition or constant-weight code of weight w has linear size if and only if its distance d is at least 2w-1. When d ≥ 2w, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of d=2w-1 has been solved previously on...
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| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/92390 http://hdl.handle.net/10220/7637 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | An optimal constant-composition or constant-weight code of weight w has linear size if and only if its distance d is at least 2w-1. When d ≥ 2w, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of d=2w-1 has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper provides a construction for quasicyclic optimal constant-composition and constant-weight codes of weight w and distance 2w-1 based on a new generalization of difference triangle sets. As a result, the sizes of optimal constant-composition codes and optimal constant-weight codes of weight w and distance 2w-1 are determined for all such codes of sufficiently large lengths. This solves an open problem of Etzion. The sizes of optimal constant-composition codes of weight w and distance 2w-1 are also determined for all w ≤ 6, except in two cases. |
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