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 |
Bibliographical note
Funding Information:The authors were supported by the National Research Foundation of Korea (NRF) grant founded by the Korea government (MEST) (2014-002731), the first named author was also supported by the National Research Foundation of Korea (NRF) grant founded by the Korea government (NRF-2013R1A1A2063240), and the second named author by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).
Publisher Copyright:
© 2016 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics