Several classes of optimal p-ary cyclic codes with minimal distance four

In this paper, by analyzing the solutions of certain equations over F 3 m , we present four classes of optimal ternary cyclic codes with parameters 3 m - 1 , 3 m - 1 - 2 m , 4 . It is shown that some recent work on this class of optimal ternary cyclic codes are special cases of our results.

[1]  Chaoping Xing,et al.  On Self-Dual Cyclic Codes Over Finite Fields , 2011, IEEE Transactions on Information Theory.

[2]  Lei Hu,et al.  A triple-error-correcting cyclic code from the Gold and Kasami-Welch APN power functions , 2010, Finite Fields Their Appl..

[3]  Tao Feng.  On cyclic codes of length $${2^{2^r}-1}$$ with two zeros whose dual codes have three weights , 2012, Des. Codes Cryptogr..

[4]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .

[5]  G. David Forney,et al.  On decoding BCH codes , 1965, IEEE Trans. Inf. Theory.

[6]  Cunsheng Ding,et al.  Five Families of Three-Weight Ternary Cyclic Codes and Their Duals , 2013, IEEE Transactions on Information Theory.

[7]  Cunsheng Ding,et al.  The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials , 2013, IEEE Transactions on Information Theory.

[8]  Cunsheng Ding,et al.  Optimal ternary cyclic codes with minimum distance four and five , 2013, Finite Fields Their Appl..

[9]  Cunsheng Ding,et al.  A q-polynomial approach to cyclic codes , 2013, Finite Fields Their Appl..

[10]  Cunsheng Ding,et al.  A Family of Five-Weight Cyclic Codes and Their Weight Enumerators , 2013, IEEE Transactions on Information Theory.

[11]  Cunsheng Ding,et al.  Optimal Ternary Cyclic Codes From Monomials , 2013, IEEE Transactions on Information Theory.

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

[13]  Cunsheng Ding,et al.  A class of three-weight cyclic codes , 2013, Finite Fields Their Appl..

[14]  Cunsheng Ding,et al.  Seven Classes of Three-Weight Cyclic Codes , 2013, IEEE Transactions on Communications.

[15]  Robert T. Chien,et al.  Cyclic decoding procedures for Bose- Chaudhuri-Hocquenghem codes , 1964, IEEE Trans. Inf. Theory.