### 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 |
---|---|

Pages (from-to) | 601-612 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 217 |

DOIs | |

Publication status | Published - 2017 Jan 30 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*217*, 601-612. https://doi.org/10.1016/j.dam.2016.09.032

}

*Discrete Applied Mathematics*, vol. 217, pp. 601-612. https://doi.org/10.1016/j.dam.2016.09.032

**t-CIS codes over GF(p) and orthogonal arrays.** / Kim, Hyun Jin; Lee, Yoonjin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - t-CIS codes over GF(p) and orthogonal arrays

AU - Kim, Hyun Jin

AU - Lee, Yoonjin

PY - 2017/1/30

Y1 - 2017/1/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84994410866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994410866&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.09.032

DO - 10.1016/j.dam.2016.09.032

M3 - Article

VL - 217

SP - 601

EP - 612

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -