On the Pless-construction and ML decoding of the (48,24,12) quadratic residue code

Esmaeili M.; Gulliver T.A.; Khandani A.K.

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On the Pless-construction and ML decoding of the (48,24,12) quadratic residue code

机译：关于（48,24,12）二次余数码的Pless构造和ML解码

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We present a method for maximum likelihood decoding of the (48,24,12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the (24,12,8) Golay code, the (48,24,12) code does not have a Pless-construction which has been an open question in the literature. It is determined that the highest minimum distance of a (48,24) binary code having a Pless (1986) construction is 10, and up to equivalence there are three such codes.

机译：我们提出了一种对（48,24,12）二次残差码进行最大似然解码的方法。此方法基于将代码投影到具有非循环Tanner图的子代码上，并通过网格图表示陪集领导者的集合。这导致两级陪集解码，可以将其视为Wagner规则的系统概括。我们证明，与（24,12,8）Golay代码不同，（48,24,12）代码没有Pless构造，这在文献中是一个未解决的问题。已确定具有Pless（1986）构造的（48,24）二进制代码的最高最小距离为10，直到等价为止，存在三个此类代码。

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来源
《IEEE Transactions on Information Theory》 |2003年第6期|p.1527-1535|共9页
作者
Esmaeili M.; Gulliver T.A.; Khandani A.K.;
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作者单位

Dept. of Math. Sci., Isfahan Univ. of Technol., Iran;

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原文格式 PDF
正文语种 eng
中图分类无线电电子学、电信技术;
关键词
maximum likelihood decoding; binary codes; Golay codes; graph theory; residue codes; linear codes; Pless based code construction; ML decoding; quadratic residue code; maximum likelihood decoding; subcode; acyclic Tanner graph; coset leaders; trellis;

机译：最大似然解码;二进制代码格雷码;图论残码线性代码;基于Pless的代码构造;ML解码;二次残基代码最大似然解码;子代码;非循环坦纳图;陪伴领导;格子;

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专利

1. The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code [J] . Houghten S.K., Lam C.W.H., Thiel L.H., IEEE Transactions on Information Theory . 2003,第1期

机译：扩展的二次余数代码是唯一的（48,24,12）自对偶双偶代码
2. An Improved Decoding Algorithm to Decode Quadratic Residue Codes Based on the Difference of Syndromes [J] . Duan Yunde, Li Yong IEEE Transactions on Information Theory . 2020,第10期

机译：一种改进的解码算法，用于基于综合征的差异解码二次残差码
3. A Scheme for Collective Encoding and Iterative Soft-Decision Decoding of Cyclic Codes of Prime Lengths: Applications to Reed–Solomon, BCH, and Quadratic Residue Codes [J] . Shu Lin, Khaled Abdel-Ghaffar, Juane Li, IEEE Transactions on Information Theory . 2020,第9期

机译：循环长度循环码的集体编码和迭代软判决解码方案：芦苇所罗门，BCH和二次残留码的应用
4. Syndrome-Weight Decoder for General Binary Quadratic Residue Codes [C] . Ming-Haw Jing, Yaotsu Chang, Zih-Heng Chen, International Conference on Information, Communications and Signal Processing . 2009

机译：一般二元二次残基码的综合体重解码器
5. On dihedral codes and the double circulant conjecture for binary extended quadratic residue codes. [D] . Musa, Mona Barakat. 2004

机译：关于二面性码和双循环二次猜想，用于二进制扩展的二次余数码。
6. Overview and Development of the Child Health and Mortality Prevention Surveillance Determination of Cause of Death (DeCoDe) Process and DeCoDe Diagnosis Standards [O] . Dianna M Blau, J Patrick Caneer, Rebecca P Philipsborn, -1

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7. On the Pless-Construction and ML Decoding of the (48, 24, 12) Quadratic Residue Code [O] . M. Esmaeili, T. A. Gulliver, A. K. Khandani 2007

机译：（48、24、12）二次残数码的Pless构造和ML解码
8. Weight Distribution of the Quadratic Residue (71,35) Code [R] . Pless, V. 1964

机译：二次残差（71,35）代码的权重分布

On the Pless-construction and ML decoding of the (48,24,12) quadratic residue code

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