The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials
dc.contributor.author | Li, Chunlei | eng |
dc.contributor.author | Li, Nian | eng |
dc.contributor.author | Helleseth, Tor | eng |
dc.contributor.author | Ding, Cunsheng | eng |
dc.date.accessioned | 2014-09-08T10:44:10Z | |
dc.date.available | 2014-09-08T10:44:10Z | |
dc.date.issued | 2014-08 | eng |
dc.identifier.issn | 0018-9448 | en_US |
dc.identifier.uri | https://hdl.handle.net/1956/8430 | |
dc.description.abstract | Let m ≥ 3 be an odd integer and p be an odd prime. In this paper, a number of classes of three-weight cyclic codes C(1,e) over Fp, which have parity-check polynomial m1(x)me (x), are presented by examining general conditions on the parameters p, m and e, where mi (x) is the minimal polynomial of π−i over Fp for a primitive element π of Fpm . Furthermore, for p ≡ 3 (mod 4) and a positive integer e satisfying (pk + 1) · e ≡ 2 (mod pm − 1) for some positive integer k with gcd(m, k) = 1, the value distributions of the exponential sums T(a, b) = ∑ x∈Fpm ωTr(ax+bxe ) and S(a, b, c) = ∑ x∈Fpm ωTr(ax+bxe +cxs ), where s = (pm − 1)/2, are determined. As an application, the value distribution of S(a, b, c) is utilized to derive the weight distribution of the cyclic codes C(1,e,s) with parity-check polynomial m1(x)me (x)ms (x). In the case of p = 3 and even e satis- fying the above condition, the dual of the cyclic code C(1,e,s) has optimal minimum distance. | en_US |
dc.language.iso | eng | eng |
dc.publisher | IEEE | en_US |
dc.relation.ispartof | <a href="http://hdl.handle.net/1956/8414" target="_blank">Sequences and Linear Codes from Highly Nonlinear Functions</a> | en_US |
dc.title | The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials | en_US |
dc.type | Peer reviewed | |
dc.type | Journal article | |
dc.description.version | acceptedVersion | en_US |
dc.rights.holder | Copyright 2014 I EEE | en_US |
dc.identifier.doi | https://doi.org/10.1109/tit.2014.2329694 | |
dc.identifier.cristin | 1163639 | |
dc.source.journal | IEEE Transactions on Information Theory | |
dc.source.40 | 60 | |
dc.source.14 | 8 | |
dc.source.pagenumber | 4710-4721 |