New Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods

Jun IMAI; Yoshinao SHIRAKI

doi:10.1093/ietfec/e88-a.10.2734

New Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods

Jun IMAI, Yoshinao SHIRAKI

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We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.10 pp.2734-2744

Publication Date: 2005/10/01

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DOI: 10.1093/ietfec/e88-a.10.2734

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coding Theory

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Jun IMAI, Yoshinao SHIRAKI, "New Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 10, pp. 2734-2744, October 2005, doi: 10.1093/ietfec/e88-a.10.2734.
Abstract: We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.10.2734/_p

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@ARTICLE{e88-a_10_2734,
author={Jun IMAI, Yoshinao SHIRAKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods},
year={2005},
volume={E88-A},
number={10},
pages={2734-2744},
abstract={We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.},
keywords={},
doi={10.1093/ietfec/e88-a.10.2734},
ISSN={},
month={October},}

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TY - JOUR
TI - New Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2734
EP - 2744
AU - Jun IMAI
AU - Yoshinao SHIRAKI
PY - 2005
DO - 10.1093/ietfec/e88-a.10.2734
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2005
AB - We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.
ER -