The weight distribution of a class of p-ary cyclic codes

For an odd prime p and two positive integers n>=3 and k with ngcd(n,k) being odd, the paper determines the weight distribution of a class of p-ary cyclic codes C over F"p with nonzeros @a^-^1, @a^-^(^p^^^k^+^1^) and @a^-^(^p^^^3^^^k^+^1^), where @a is a primitive element of F"p"^"n.

[1]  Carl Bracken,et al.  New Families of Triple Error Correcting Codes with BCH Parameters , 2008, ArXiv.

[2]  Qing Xiang.  Maximally Nonlinear Functions and Bent Functions , 1999, Des. Codes Cryptogr..

[3]  Lei Hu,et al.  Generalized Kasami Sequences: The Large Set , 2005, IEEE Transactions on Information Theory.

[4]  H. Hollmann,et al.  On Binary Cyclic Codes With Few Weights , 2001 .

[5]  Claude Carlet,et al.  Boolean Functions for Cryptography and Error-Correcting Codes , 2010, Boolean Models and Methods.

[6]  O. S. Rothaus,et al.  On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[7]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[8]  Robert S. Coulter,et al.  Planar Functions and Planes of Lenz-Barlotti Class II , 1997, Des. Codes Cryptogr..

[9]  Cunsheng Ding,et al.  The weight distribution of a class of linear codes from perfect nonlinear functions , 2006, IEEE Transactions on Information Theory.

[10]  T. Kasami.  WEIGHT DISTRIBUTION OF BOSE-CHAUDHURI-HOCQUENGHEM CODES. , 1966 .

[11]  Claude Carlet,et al.  Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems , 1998, Des. Codes Cryptogr..

[12]  Rudolf Lide,et al.  Finite fields , 1983 .

[13]  Xiang-Dong Hou,et al.  Explicit evaluation of certain exponential sums of binary quadratic functions , 2007, Finite Fields Their Appl..

[14]  Cunsheng Ding,et al.  A family of skew Hadamard difference sets , 2006, J. Comb. Theory, Ser. A.

[15]  Hans Dobbertin.  Another Proof of Kasami's Theorem , 1999, Des. Codes Cryptogr..

[16]  Cunsheng Ding,et al.  Highly nonlinear mappings , 2004, J. Complex..

[17]  Cunsheng Ding,et al.  Linear codes from perfect nonlinear mappings and their secret sharing schemes , 2005, IEEE Transactions on Information Theory.

[18]  Cunsheng Ding,et al.  Systematic authentication codes from highly nonlinear functions , 2004, IEEE Transactions on Information Theory.

[19]  Xiang-Dong Hou,et al.  p-Ary and q-ary versions of certain results about bent functions and resilient functions , 2004, Finite Fields Their Appl..

[20]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[21]  Keqin Feng,et al.  Weight distribution of some reducible cyclic codes , 2008, Finite Fields Their Appl..