ON GRAY IMAGES OF CONSTACYCLIC CODES OVER THE FINITE RING F2 + u1 F2 + u2 F2

Year 2019, Volume: 9 Issue: 4, 876 - 881, 01.12.2019

M. ÖZKAN A. DERTLİ Y. CENGELLENMİS

Abstract

We introduce the nite ring F2 + u1F2 + u2F2, u1 2 = u1 ; u2 2 = 0 ; u1:u2 = u2:u1 = 0 which is not a nite chain ring. We focus on 1 + u2 -constacyclic codes over F2 + u1F2 + u2F2 of odd length. We prove that the Gray image of a linear 1 + u2 -constacyclic code over F2 + u1F2 + u2F2 of odd length n is a quasi-cyclic code of index 4 and length 4n over F2.

Keywords

Constacylic code, Gray image.

References

• M. C. Amarra, F. R. Nemenzo, (2008), On (1 − u)-cyclic codes over Fpk+ uFpk, Applied Mathematics Letters, 21, pp. 1129-1133.
• Y. Cengellenmis, (2009), On (1 + um)-cyclic codes over F+ uF2+ ... + umF2, Int J.Contemp. Math Sciences, 20 (4), pp. 987-992.
• S. Karadeniz, B. Yldz, (2011), On (1 − v)-constacyclic codes over F2+ uF2+ vF2+ uvF2, Journal of the Franklin Institude , 348, pp. 2625-2632.
• J.F. Qian, L. N. Zhang, S. X. Zhu, (2006), ( (1 + u)-constacyclic and cyclic codes over F2+ uF2, Applied Mathematics Letters 19, pp. 820-823.
• J. F. Qian, L. N. Zhang, S. X. Zhu, (2006), Constacyclic and cyclic codes over F2+ uF2+ u2F2, IEICE Trans.Fundamentals, 89-a (6), pp. 1863-1865.
• J.Wolfmann, (1999), Negacyclic and cyclic codes over Z4, IEEE Trans. Inf. Theory, 45, pp. 2527-2532.
• Xu Xioafang, (2013), (1+v)-constacyclic codes over F2+ uF2+ vF , Computer Engineering and Applications, 49 (12), pp. 77-79.