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SKEW CYCLIC CODES OVER Fp + vFp

  • Gao, Jian (School of Sciense, Shandong University of Technology)
  • Received : 2012.06.14
  • Accepted : 2012.10.10
  • Published : 2013.05.30

Abstract

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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Cited by

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  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