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

Abstract

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.

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

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.

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.

Details

Primary Language English
Journal Section Research Article
Authors

M. ÖZKAN This is me
Department of Mathematics, Trakya University, Edirne, Turkey


A. DERTLİ This is me
Department of Mathematics, Ondokuz Mayis University, Samsun, Turkey


Y. CENGELLENMİS This is me
Department of Mathematics, Trakya University, Edirne, Turkey

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760960, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {876 - 881}, title = {ON GRAY IMAGES OF CONSTACYCLIC CODES OVER THE FINITE RING F2 + u1 F2 + u2 F2}, key = {cite}, author = {Özkan, M. and Dertli, A. and Cengellenmis, Y.} }