TY - JOUR

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

AU - Kim, Hyun Jin

AU - Lee, Yoonjin

N1 - 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.

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.

KW - Complementary information set code

KW - Correlation immune

KW - Equivalence

KW - Optimal code

KW - Orthogonal array

KW - Self-dual code

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

U2 - 10.1016/j.dam.2016.09.032

DO - 10.1016/j.dam.2016.09.032

M3 - Article

AN - SCOPUS:84994410866

SN - 0166-218X

VL - 217

SP - 601

EP - 612

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -