IEICE TRANSACTIONS on Fundamentals
On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements
Summary :
The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.9 pp.2337-2340
- Publication Date
- 2006/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e89-a.9.2337
- Type of Manuscript
- Special Section LETTER (Special Section on Sequence Design and its Application in Communications)
- Category
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Keyword
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Junru ZHENG, Takayasu KAIDA, "On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 9, pp. 2337-2340, September 2006, doi: 10.1093/ietfec/e89-a.9.2337.
Abstract: The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.9.2337/_p
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@ARTICLE{e89-a_9_2337,
author={Junru ZHENG, Takayasu KAIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements},
year={2006},
volume={E89-A},
number={9},
pages={2337-2340},
abstract={The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.},
keywords={},
doi={10.1093/ietfec/e89-a.9.2337},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2337
EP - 2340
AU - Junru ZHENG
AU - Takayasu KAIDA
PY - 2006
DO - 10.1093/ietfec/e89-a.9.2337
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2006
AB - The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.
ER -
English
