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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Untuk perdana ganjil q dan integer m≤q, kita boleh membina matriks semakan pariti kuasi-kitaran biasa HI(m,q) yang menentukan kod blok linear CI(m,q), dipanggil an tatasusunan yang tidak betul kod. Dalam surat ini, kami membuktikan jarak minimum CI(4,q) adalah sama dengan 10 untuk mana-mana q≥11. Di samping itu, kami membuktikan jarak minimum CI(5,q) bersempadan atas dengan 12 untuk mana-mana q≥11 dan jangkaan sempadan atas adalah ketat.
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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Salinan
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
Salinan
@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},}
Salinan
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 -