Computing methods for the weight distributions of linear block codes and the weight distributions of the extended binary primitive BCH codes of lengths 64 and 128 線形ブロック符号の重み分布計算法, 及び符号長64, 128の2元原始拡大BCH符号の重み分布
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Bibliographic Information
- Title
-
Computing methods for the weight distributions of linear block codes and the weight distributions of the extended binary primitive BCH codes of lengths 64 and 128
- Other Title
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線形ブロック符号の重み分布計算法, 及び符号長64, 128の2元原始拡大BCH符号の重み分布
- Author
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出崎, 善久
- Author(Another name)
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デサキ, ヨシヒサ
- University
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大阪大学
- Types of degree
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博士 (工学)
- Grant ID
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乙第7262号
- Degree year
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1997-06-30
Note and Description
博士論文
Table of Contents
- Abstract / p1 (0003.jp2)
- Contents / p6 (0006.jp2)
- 1 Introduction / p1 (0007.jp2)
- 2 A Computing Method Using the Trellis Diagram of a Linear Block Code / p7 (0010.jp2)
- 2.1 Minimal Trellis Diagram / p7 (0010.jp2)
- 2.2 Two Algorithms for Computing the Weight Distribution / p8 (0011.jp2)
- 2.3 Complexity analysis of the Two Algorithms / p11 (0012.jp2)
- 2.4 Example / p15 (0014.jp2)
- 2.5 Symmetric Property of Minimal Trellis Diagram / p17 (0015.jp2)
- 2.6 An Improved Computing Method by Using a Trellis Diagram / p20 (0017.jp2)
- 3 A Computing Method Using an Invariant Property of a Linear Block Code for Permutation Groups / p21 (0017.jp2)
- 3.1 Outline of the Method / p21 (0017.jp2)
- 3.2 Partition of the Cosets with respect to the Cyclic Group / p22 (0018.jp2)
- 3.3 Partition of the Cosets with respect to the Affine Group / p24 (0019.jp2)
- 4 The Weight Distributions of Extended Codes of Binary Primitive BCH Codes of Lengths 64 and 128 / p27 (0020.jp2)
- 4.1 Computing Method / p27 (0020.jp2)
- 4.2 Weight Distributions / p31 (0022.jp2)
- 4.3 Probability of an Undetectable Error / p38 (0026.jp2)
- 5 Upper and Lower Bounds on the Undetected Error Probability of Binary Codes Derived from Shortened Reed-Solomon Codes / p40 (0027.jp2)
- 5.1 Binary Weight Distribution of a Code over GF(〔数式〕) / p40 (0027.jp2)
- 5.2 The Number of Codewords with Small Weights of Some Shortened Reed-Solomon Codes / p42 (0028.jp2)
- 5.3 Upper and Lower Bounds on the Probability of an Undetectable Error / p51 (0033.jp2)
- 6 Conclusions / p55 (0035.jp2)
- References / p59 (0037.jp2)