On the Gray images of some constacyclic codes over Fp + uFp + u2Fp

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp + uFp + u2Fp and codes over Fp is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1+u+u2)-constacyclic code over Fp + uFp + u2Fp of length n is a repeated-root cyclic code over Fp of length pn. Furthermore, some examples of optimal linear cyclic codes over F3 from (1 + u + u2)-constacyclic codes over F3 + uF3 + u2F3 are given.

[1]  Gerardo Vega,et al.  A Generalization of Negacyclic Codes , 2001, Electron. Notes Discret. Math..

[2]  Shixin Zhu,et al.  Constacyclic and Cyclic Codes over F2 + uF2 + u2F2 , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[3]  Jacques Wolfmann,et al.  Negacyclic and cyclic codes over Z4 , 1999, IEEE Trans. Inf. Theory.

[4]  Shixin Zhu,et al.  (1+λu)-Constacyclic codes over Fp[u]/〈um〉 , 2010, J. Frankl. Inst..

[5]  J. Wolfman.  Negacyclic and cyclic codes over Z/sub 4/ , 1999 .

[6]  Haifeng,et al.  （1-uv）-CONSTACYCLIC CODES OVER Fp＋uFp＋vFp＋uvFp , 2014 .

[7]  Y. Cengellenmis.  On some special codes over Fp + uFp + u2Fp , 2011, Appl. Math. Comput..

[8]  Christine Bachoc,et al.  Applications of Coding Theory to the Construction of Modular Lattices , 1997, J. Comb. Theory A.

[9]  Suat Karadeniz,et al.  Cyclic codes over F2+uF2+vF2+uvF2 , 2011, Des. Codes Cryptogr..

[10]  Shixin Zhu,et al.  A family of constacyclic codes over F2 + uF2 + vF2 + uvF2 , 2012, J. Syst. Sci. Complex..

[11]  Jacques Wolfmann.  Binary images of cyclic codes over Z4 , 2001, IEEE Trans. Inf. Theory.

[12]  Suat Karadeniz,et al.  (1+v)-Constacyclic codes over F2+uF2+vF2+uvF2 , 2011, J. Frankl. Inst..

[13]  Shixin Zhu,et al.  (1 − uv)-constacyclic codes over $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p $ , 2014 .

[14]  Shixin Zhu,et al.  A class of constacyclic codes over Fp+vFp and its Gray image , 2011, Discret. Math..

[15]  Shixin Zhu,et al.  Cyclic Codes over Fp + uFp+ ··· +uk-1 Fp , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[16]  Taher Abualrub,et al.  Constacyclic codes over F2+uF2 , 2009, J. Frankl. Inst..

[17]  Maria Carmen V. Amarra,et al.  On (1-u) -cyclic codes over Fpk + uFpk , 2008, Appl. Math. Lett..

[18]  San Ling,et al.  Zpk+1-Linear codes , 2002, IEEE Trans. Inf. Theory.

[19]  Shixin Zhu,et al.  (1+u) constacyclic and cyclic codes over F2+uF2 , 2006, Appl. Math. Lett..