有限鏈環(huán)上一類常循環(huán)碼的距離
doi: 10.11999/JEIT160392
基金項目:
國家自然科學(xué)基金(61370089, 60973125)，東南大學(xué)國家移動通信研究實驗室開放研究基金(2014D04)，安徽省自然科學(xué)基金(1508085SQA198)
On Distances of Family of Constacyclic Codes over Finite Chain Rings
Funds:
The National Natural Science Foundation of China (61370089, 60973125), The Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2014D04), The Natural Science Foundation of Anhui Province (1508085SQA198)
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摘要: 在編碼理論中，線性碼的(最小)距離是一個極其重要的參數(shù)，它決定了碼的糾錯能力。設(shè)R為任一有限交換鏈環(huán)， a為其最大理想的一個生成元， R*為R的乘法單位群。對于任意wR*，該文利用R上任意長度的(1+aw)-常循環(huán)碼的生成結(jié)構(gòu)，通過計算這類碼的高階撓碼，得到了R上任意長度的(1+aw)-常循環(huán)碼的漢明距離，并研究了這類常循環(huán)碼的齊次距離。這給編譯有限鏈環(huán)上此類常循環(huán)碼提供了重要的理論依據(jù)。
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關(guān)鍵詞:
- 常循環(huán)碼 /
- 有限鏈環(huán) /
- 漢明距離 /
- 齊次距離
Abstract: In coding theory, the (minimum) distance of a code is a very important invariant, which always determines the error-correcting capability of the code. Let R be an arbitrary commutative finite chain ring, a is a generator of the unique maximal ideal andR* is the multiplicative group of units of R. In this paper, for any wR*, by using the generator polynomials of (1+aw)-constacyclic codes of any length over R, higher torsion codes of such codes are calculated. The Hamming distance of all(1+aw)-constacyclic codes of any length overR is determined and the exact homogeneous distance of some such codes is obtained. The result provides a theoretical basis for encoding and decoding for such constacyclic codes.-
Key words:
- Constacyclic codes /
- Finite chain rings /
- Hamming distance /
- Homogeneous distance
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