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On the Weight Distributions of Two Classes of Cyclic Codes.
- Source :
- IEEE Transactions on Information Theory; Dec2008, Vol. 54 Issue 12, p5332-5344, 13p
- Publication Year :
- 2008
-
Abstract
- Let q = p<superscript>m</superscript> where p is an odd prime, m ≥ 2, and 1 ≤ k ≤ m - 1. Let Tr be the trace mapping from F<subscript>q</subscript> to F<subscript>p</subscript> and (ζ<subscript>p</subscript> = e 2π i/p be a primitive pth root of unity. In this paper, we determine the value distribution of the following exponential sums: Σ x ϵ F<subscript>q</subscript> χ (αx<superscript>p</superscript><superscript>k+1</superscript> + βx²) (α, β ϵ F<subscript>q</subscript>) where <subscript>χ</subscript>(x) = ζ<subscript>p</subscript><superscript>Tr(x)</superscript> is the canonical additive character of F<subscript>q</subscript>. As applications, we have the following. 1) We determine the weight distribution of the cyclic codes C<subscript>1</subscript> and C<subscript>2</subscript> over F<subscript>p<superscript>t</superscript></subscript> with parity-check polynomial h<subscript>2</subscript> (x)h<subscript>3</subscript> (x) and h<subscript>1</subscript> (x)h<subscript>2</subscript> (x)h<subscript>3</subscript> (x), respectively, where t is a divisor of d = gcd (m, k), and h<subscript>1</subscript> (x), h<subscript>2</subscript> (x), and h<subscript>3</subscript> (x) are the minimal polynomials of π<superscript>-1</superscript>, π<superscript>-2</superscript>, and π<superscript>-(P<superscript>k</superscript>+1)</superscript> over F<subscript>P<superscript>t</superscript></subscript> respectively, for a primitive element π of F<subscript>q</subscript>. 2) We determine the correlation distribution between two m-sequences of period q -1. Moreover, we find a new class of p-ary bent functions. This paper extends the results in Feng and Luo (2008). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 54
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 35843427
- Full Text :
- https://doi.org/10.1109/TIT.2008.2006424