On the Minimum Distance of Some Improper Array Codes

Haiyang LIU  Lianrong MA  Hao ZHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A    No.12    pp.2021-2026
Publication Date: 2019/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.2021
Type of Manuscript: LETTER
Category: Coding Theory
minimum distance,  proper array (PA) codes,  improper array (IA) codes,  

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For an odd prime q and an integer mq, 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.