t-CIS codes over GF(p) and orthogonal arrays

Hyun Jin Kim, Yoonjin Lee

Research output: Contribution to journalArticle

Abstract

We first show that orthogonal arrays over GF(p) can be explicitly constructed from t-CIS codes over GF(p), where t-CIS codes are CIS codes of order t≥2. With this motivation, we are interested in developing methods of constructing t-CIS codes over GF(p). We present two types of constructions; the first one is a “t-extension method” which is finding t-CIS codes over GF(p) of length tn from given (t−1)-CIS codes over GF(p) of length (t−1)n for t>2, and the second one is a “building-up type construction” which is finding t-CIS codes over GF(p) of length t(n+1) from given t-CIS codes over GF(p) of length tn. Furthermore, we find a criterion for checking equivalence of t-CIS codes over GF(p). We find inequivalent t-CIS codes over GF(p) of length n for t=3,4, n=9,12,16, and p=3,5,7 using our construction and criterion, and corresponding orthogonal arrays are found. We point out that 171t-CIS codes we found are optimal codes.

Original language English 601-612 12 Discrete Applied Mathematics 217 https://doi.org/10.1016/j.dam.2016.09.032 Published - 2017 Jan 30

Orthogonal Array
Optimal Codes
Equivalence

All Science Journal Classification (ASJC) codes

• Discrete Mathematics and Combinatorics
• Applied Mathematics

Cite this

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title = "t-CIS codes over GF(p) and orthogonal arrays",
abstract = "We first show that orthogonal arrays over GF(p) can be explicitly constructed from t-CIS codes over GF(p), where t-CIS codes are CIS codes of order t≥2. With this motivation, we are interested in developing methods of constructing t-CIS codes over GF(p). We present two types of constructions; the first one is a “t-extension method” which is finding t-CIS codes over GF(p) of length tn from given (t−1)-CIS codes over GF(p) of length (t−1)n for t>2, and the second one is a “building-up type construction” which is finding t-CIS codes over GF(p) of length t(n+1) from given t-CIS codes over GF(p) of length tn. Furthermore, we find a criterion for checking equivalence of t-CIS codes over GF(p). We find inequivalent t-CIS codes over GF(p) of length n for t=3,4, n=9,12,16, and p=3,5,7 using our construction and criterion, and corresponding orthogonal arrays are found. We point out that 171t-CIS codes we found are optimal codes.",
author = "Kim, {Hyun Jin} and Yoonjin Lee",
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t-CIS codes over GF(p) and orthogonal arrays. / Kim, Hyun Jin; Lee, Yoonjin.

In: Discrete Applied Mathematics, Vol. 217, 30.01.2017, p. 601-612.

Research output: Contribution to journalArticle

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AU - Kim, Hyun Jin

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