The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Pour un nombre premier impair q et un entier m≤q, nous pouvons construire une matrice de contrôle de parité quasi-cyclique régulière HI(m,q) qui spécifie un code de bloc linéaire CI(m,q), appelé un tableau inapproprié code. Dans cette lettre, nous prouvons la distance minimale de CI(4,q) est égal à 10 pour tout q≥11. De plus, nous prouvons la distance minimale de CI(5,q) est limité en haut par 12 pour tout q≥11 et je suppose que la limite supérieure est serrée.
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
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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},}
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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 -