A Note on the Shift Bound for Cyclic Codes by the DFT

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概要

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• For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by their defining set, and new simple derivation of the shift bound using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.

• 2010-11-01

著者

• Kaida Takayasu

  Department Of Information And Computer Sciences Faculty Of Humanity-oriented Science And Engineering

• ZHENG Junru

  Department of Human Development, Faculty of Human Sciences, Kyushu Women's University

• Zheng Junru

  Department Of Human Development Faculty Of Human Sciences Kyushu Women's University

関連論文

• A Note on the Shift Bound for Cyclic Codes by the DFT
• Value Distribution of Linear Complexity for p-Ary Periodic Sequences with Period p^n, p a Prime
• Some Properties of the Schaub Bound and Its Improvement for Cyclic Codes
• On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements(Sequence Design and its Application in Communications)
• A Note on Decoding Algorithm by Calculation of Schaub Bound for Cyclic Codes
• On Relationship between the Boston Bound and Well-Known Bounds for Cyclic Codes
• An Improvement of the Hartmann-Tzeng Bound for Cyclic Codes and Their Binary and Short Examples
• Construction of Independent Set and Its Application for Designed Minimum Distance
• On Constant-Weight Multi-Valued Sequences from Cyclic Difference Sets

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