| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Campinas - Brazil
[2] Univ Alacant, Dept Matemat, Alacant - Spain
[3] Carleton Univ, Sch Math & Stat, Ottawa, ON - Canada
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Advances in Mathematics of Communications; v. 14, n. 3, p. 437-453, AUG 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we construct F-2-linear codes over F-2(b) with length n and dimension n - r where n = rb. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime p, let n = p - 1 and utilize a partition of Z(n). Then we apply a Zech logarithm to the elements of these sets and use the results to construct an index array which represents the parity-check matrix of the code. These codes are always cyclic and the density of the parity-check and the generator matrices decreases to 0 as n grows (for a fixed r). When r = 2 we prove that these codes are always maximum distance separable. For higher r some of them retain this property. (AU) | |
| FAPESP's process: | 16/50476-0 - Efficiency and security of pre and post quantum cryptographic methods: theory and applications |
| Grantee: | Ricardo Dahab |
| Support Opportunities: | Regular Research Grants |