Optimal <em>p</em>-ary Codes from Constacyclic Codes over a Non-chain Ring <em>R</em>

SHI Minjia

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Article Navigation > Chinese Journal of Electronics > 2014 > 23(4): 773-777

SHI Minjia, “Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 773-777, 2014,

Citation:

SHI Minjia, “Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 773-777, 2014,

SHI Minjia, “Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 773-777, 2014,

Citation:

SHI Minjia, “Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 773-777, 2014,

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Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R

SHI Minjia

School of Mathematical Sciences of Anhui University, Hefei 230601, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61202068), Talents Youth Fund of Anhui Province Universities (No.2012SQRL020ZD).

Received Date: 2013-09-01
Rev Recd Date: 2014-06-01
Publish Date: 2014-10-05

Abstract

Abstract

This paper is devoted to the study of constacyclic codes over a non-chain ring R. The generator polynomials of all constacyclic codes over R are characterized and their dual codes are also determined. We also introduce a Gray map. It is proved that the image of a v-constacyclic code of length n over R under the Gray map is a cyclic code of length 2n over a field with p elements, where p is odd prime. Moreover, we obtain a substantial number of optimal p-ary linear (cyclic) codes, in terms of their parameters, via the Gray map.
- Generator polynomial,
- Constacyclic code,
- Gray map,
- Dual code

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References(9)

References

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