Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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SKEW CYCLIC CODES OVER Fp + vFp

  • Gao, Jian (School of Sciense, Shandong University of Technology)
  • 투고 : 2012.06.14
  • 심사 : 2012.10.10
  • 발행 : 2013.05.30
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초록

In this paper, we study a special class of linear codes, called skew cyclic codes, over the ring $R=F_p+vF_p$, where $p$ is a prime number and $v^2=v$. We investigate the structural properties of skew polynomial ring $R[x,{\theta}]$ and the set $R[x,{\theta}]/(x^n-1)$. Our results show that these codes are equivalent to either cyclic codes or quasi-cyclic codes. Based on this fact, we give the enumeration of distinct skew cyclic codes over R.

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참고문헌

  1. D. Boucher and F. Ulmer, Coding with skew polynoial rings, J. Symb. Comput 44 (2009), 1644-1656. https://doi.org/10.1016/j.jsc.2007.11.008
  2. D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Eng. Commun. Comput 18 (2007), 379-389. https://doi.org/10.1007/s00200-007-0043-z
  3. I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Inf. Coding Theory 2 (2011), 10-20. https://doi.org/10.1504/IJICOT.2011.044674
  4. M. Bhaintwal, Skew quasi-cyclic codes over Galois rings, Des. Codes Cryptogr (2011), DOI10.1007/s10623-011-9494-0.
  5. S. Zhu and Y. Wang, A class of constacyclic codes over $F_p$ + $vF_p$ and its Gray image, Discrete. Math 311 (2011), 2677-2682. https://doi.org/10.1016/j.disc.2011.08.015
  6. T. Abualrub, A. Ghrayeb, N. Aydim and I. Siap, On the construction of skew quasi-cyclic codes, IEEE. Trans. Inform. Theory 56(2010), 2081-2090. https://doi.org/10.1109/TIT.2010.2044062

피인용 문헌

  1. On the linear codes over the ring Rp vol.08, pp.02, 2016, https://doi.org/10.1142/S1793830916500361
  2. Skew-cyclic codes over $$B_k$$ B k 2017, https://doi.org/10.1007/s12190-017-1095-2
  3. Some results on the linear codes over the finite ring F2+v1F2+⋯+vrF2 vol.14, pp.01, 2016, https://doi.org/10.1142/S021974991650012X
  4. On skew cyclic codes over a semi-local ring vol.07, pp.04, 2015, https://doi.org/10.1142/S1793830915500421
  5. Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$ vol.8, pp.3, 2014, https://doi.org/10.3934/amc.2014.8.313
  6. ΘS-cyclic codes overAk vol.1, pp.1, 2016, https://doi.org/10.1080/23799927.2016.1146800
  7. Skew cyclic codes over Fq + uFq + vFq 2017, https://doi.org/10.1142/S1793557118500729
  8. Skew cyclic and skew constacyclic codes over the ring 𝔽p + u1𝔽p + ⋯ + u2m𝔽p pp.1793-7183, 2018, https://doi.org/10.1142/S1793557119500839
  9. Skew quasi cyclic codes over 𝔽q + v𝔽q pp.1793-6829, 2018, https://doi.org/10.1142/S0219498819500774
  10. Skew Cyclic Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$ vol.ea98, pp.8, 2013, https://doi.org/10.1587/transfun.e98.a.1845
  11. On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ vol.11, pp.2, 2013, https://doi.org/10.32513/tbilisi/1529460020
  12. SKEW CYCLIC CODES OVER 𝔽p + v𝔽p + v2𝔽p vol.55, pp.6, 2018, https://doi.org/10.4134/bkms.b160535