## 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 |
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Pages (from-to) | 601-612 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 217 |

DOIs | |

State | Published - 30 Jan 2017 |

### Bibliographical note

Publisher Copyright:© 2016 Elsevier B.V.

## Keywords

- Complementary information set code
- Correlation immune
- Equivalence
- Optimal code
- Orthogonal array
- Self-dual code