環(huán)Z4上線性循環(huán)碼的深度譜
On the Depth Spectrums of Linear Cyclic Codes on Ring Z4
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摘要: Etzion定義并研究了域Fq上線性碼的深度譜，該文研究了環(huán)Z4上線性碼與線性循環(huán)碼的深度譜，證明了4k12k2型線性碼的深度譜至少含有k1+k2個(gè)非零值，并給出了一類4k型線性循環(huán)碼的深度譜為{n,n-1, ,n-k+1} 。
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關(guān)鍵詞:
- 線性碼;線性循環(huán)碼;深度;深度譜
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} . -
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. 糾錯(cuò)碼的深度分布在其周期分布研究中的應(yīng)用. 應(yīng)用科學(xué)學(xué)報(bào)，2001, 19(3): 189-192.[5]Wan Z X. Quaternary Codes, Singapore: World Scientific, 1997, 1-9: 96-98.[6]朱士信. 線性碼的對稱形式的Macwilliams恒等式[J].電子與信息學(xué)報(bào).2003, 25(7):901-906瀏覽[7]楊善林，朱士信，童宏璽. 兩種計(jì)算 環(huán)上碼字深度的遞歸算法. 中國科技大學(xué)學(xué)報(bào)，2004, 34(6): 655-660. -
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