On Cyclic Codes with Length 2pe over Finite Fields

PANG Binbin; ZHU Shixin; SUN Zhonghua

doi:10.1049/cje.2020.05.012

Volume 29 Issue 4

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PANG Binbin, ZHU Shixin, SUN Zhonghua, “On Cyclic Codes with Length 2pe over Finite Fields,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 672-677, 2020, doi: 10.1049/cje.2020.05.012

Citation:

PANG Binbin, ZHU Shixin, SUN Zhonghua, “On Cyclic Codes with Length 2p^e over Finite Fields,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 672-677, 2020, doi: 10.1049/cje.2020.05.012

PANG Binbin, ZHU Shixin, SUN Zhonghua, “On Cyclic Codes with Length 2pe over Finite Fields,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 672-677, 2020, doi: 10.1049/cje.2020.05.012

Citation:

PANG Binbin, ZHU Shixin, SUN Zhonghua, “On Cyclic Codes with Length 2p^e over Finite Fields,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 672-677, 2020, doi: 10.1049/cje.2020.05.012

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On Cyclic Codes with Length 2p^e over Finite Fields

doi: 10.1049/cje.2020.05.012

School of Mathematics, Hefei University of Technology, Hefei 230601, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61772168, No.61572168) and the Natural Science Foundation of Anhui Province (No.1708085QA01, No.2008085QA04).

Received Date: 2019-06-17
Rev Recd Date: 2020-01-10
Publish Date: 2020-07-10

Abstract

Abstract

Cyclic codes are an important class of linear codes. Cyclic codes are applied in data storage, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. We utilize the cyclotomy of order 2 to study the cyclic codes with length n=2p^e and dimension k=n/2=p^e. The cyclic codes from our construction are either optimal or almost optimal among all cyclic codes with the same length and dimension. We get the enumeration of these cyclic codes and study the hull of cyclic codes of length n over F_q. We obtain the range of ℓ=dim(Hull(C)). Finally, we construct and enumerate cyclic codes of length n having hull of given dimension.
- Cyclic codes,
- Cyclotomy,
- Hull,
- Primitive root

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References(30)

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