IEICE TRANSACTIONS on Fundamentals
On the Minimum Distance of Some Improper Array Codes
Summary :
For an odd prime q and an integer m≤q, we can construct a regular quasi-cyclic parity-check matrix HI(m,q) that specifies a linear block code CI(m,q), called an improper array code. In this letter, we prove the minimum distance of CI(4,q) is equal to 10 for any q≥11. In addition, we prove the minimum distance of CI(5,q) is upper bounded by 12 for any q≥11 and conjecture the upper bound is tight.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.12 pp.2021-2026
- Publication Date
- 2019/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.2021
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Haiyang LIU
the Institute of Microelectronics of Chinese Academy of Sciences
Lianrong MA
Tsinghua University
Hao ZHANG
the Institute of Microelectronics of Chinese Academy of Sciences
Keyword
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Haiyang LIU, Lianrong MA, Hao ZHANG, "On the Minimum Distance of Some Improper Array Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 12, pp. 2021-2026, December 2019, doi: 10.1587/transfun.E102.A.2021.
Abstract: For an odd prime q and an integer m≤q, we can construct a regular quasi-cyclic parity-check matrix HI(m,q) that specifies a linear block code CI(m,q), called an improper array code. In this letter, we prove the minimum distance of CI(4,q) is equal to 10 for any q≥11. In addition, we prove the minimum distance of CI(5,q) is upper bounded by 12 for any q≥11 and conjecture the upper bound is tight.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.2021/_p
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@ARTICLE{e102-a_12_2021,
author={Haiyang LIU, Lianrong MA, Hao ZHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Minimum Distance of Some Improper Array Codes},
year={2019},
volume={E102-A},
number={12},
pages={2021-2026},
abstract={For an odd prime q and an integer m≤q, we can construct a regular quasi-cyclic parity-check matrix HI(m,q) that specifies a linear block code CI(m,q), called an improper array code. In this letter, we prove the minimum distance of CI(4,q) is equal to 10 for any q≥11. In addition, we prove the minimum distance of CI(5,q) is upper bounded by 12 for any q≥11 and conjecture the upper bound is tight.},
keywords={},
doi={10.1587/transfun.E102.A.2021},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - On the Minimum Distance of Some Improper Array Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2021
EP - 2026
AU - Haiyang LIU
AU - Lianrong MA
AU - Hao ZHANG
PY - 2019
DO - 10.1587/transfun.E102.A.2021
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2019
AB - For an odd prime q and an integer m≤q, we can construct a regular quasi-cyclic parity-check matrix HI(m,q) that specifies a linear block code CI(m,q), called an improper array code. In this letter, we prove the minimum distance of CI(4,q) is equal to 10 for any q≥11. In addition, we prove the minimum distance of CI(5,q) is upper bounded by 12 for any q≥11 and conjecture the upper bound is tight.
ER -
English
