On the Depth Spectrums of Linear Cyclic Codes on Ring Z4

Zhu Shi-xin; Yang Shan-lin; Tong Hong-xi

Volume 27 Issue 10

Oct. 2005

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Zhu Shi-xin, Yang Shan-lin, Tong Hong-xi. On the Depth Spectrums of Linear Cyclic Codes on Ring Z4[J]. Journal of Electronics & Information Technology, 2005, 27(10): 1597-1599.

Citation:

Zhu Shi-xin, Yang Shan-lin, Tong Hong-xi. On the Depth Spectrums of Linear Cyclic Codes on Ring Z4[J]. Journal of Electronics & Information Technology, 2005, 27(10): 1597-1599.

Zhu Shi-xin, Yang Shan-lin, Tong Hong-xi. On the Depth Spectrums of Linear Cyclic Codes on Ring Z4[J]. Journal of Electronics & Information Technology, 2005, 27(10): 1597-1599.

Citation:

Zhu Shi-xin, Yang Shan-lin, Tong Hong-xi. On the Depth Spectrums of Linear Cyclic Codes on Ring Z4[J]. Journal of Electronics & Information Technology, 2005, 27(10): 1597-1599.

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On the Depth Spectrums of Linear Cyclic Codes on Ring Z4

Received Date: 2004-06-28
Rev Recd Date: 2004-12-09
Publish Date: 2005-10-19

Abstract

Abstract

Etzion defined and studied the depth spectrums of linear codes on field Fq. In this correspondence, the depth spectrums of linear codes and linear cyclic codes on ring Z4 are studied, and it is proved that the depth spectrum of linear code of type 4k12k2 has at least k1+k2 nonzero values, and the depth spectrum of linear cyclic code of type 4k is {n,n-1, ,n-k+1} .

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References(1)

References

Etzion T. The depth distributionA new characterization for linear codes. IEEE Trans. on Info.Thory. 1997, IT-43(4): 1361-1363.[2]Mitchell C J. On integer-valued rational polynomials and depth distributions of binary codes. IEEE Trans. on Info. Theory, 1998, IT-44(7): 3146-3150.[3]Luo Y, Fu Fangwei, Victor K V Wei. On the depth distribution of linear codes. IEEE Trans. on Info. Theory. 2000, IT-46(6): 2197-2203.[4]岳殿武，Shwedyk E. 纠错码的深度分布在其周期分布研究中的应用. 应用科学学报，2001, 19(3): 189-192.[5]Wan Z X. Quaternary Codes, Singapore: World Scientific, 1997, 1-9: 96-98.[6]朱士信. 线性码的对称形式的Macwilliams恒等式[J].电子与信息学报.2003, 25(7):901-906浏览[7]杨善林，朱士信，童宏玺. 两种计算环上码字深度的递归算法. 中国科技大学学报，2004, 34(6): 655-660.

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