TY - JOUR

T1 - Construction of isodual codes over GF(q)

AU - Kim, Hyun Jin

AU - Lee, Yoonjin

N1 - Funding Information:
The first named author was supported by the National Research Foundation of Korea (NRF) grant founded by the Korea government (NRF-2013R1A1A2063240), and the second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827) and also by the National Research Foundation of Korea (NRF) grant founded by the Korea government (MEST) (2014-002731).
Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We develop a construction method of isodual codes over GF(q), where q is a prime power; we construct isodual codes over GF(q) of length 2n+2 from isodual codes over GF(q) of length 2n. Using this method, we find some isodual codes over GF(q), where q=2,3 and 5. In more detail, we obtain binary isodual codes of lengths 32, 34, 36, 38, and 40, where all these codes of lengths 32, 34, and 36 are optimal and some codes of length 38 are optimal. We note that all these binary isodual codes are not self-dual codes, and in particular, in the case of length 38 all their weight enumerators are different from those of binary self-dual codes of the same length; in fact, four binary isodual codes of length 38 are formally self-dual even codes. We construct isodual codes over GF(3) and GF(5) of lengths 4, 6, and 8 as well.

AB - We develop a construction method of isodual codes over GF(q), where q is a prime power; we construct isodual codes over GF(q) of length 2n+2 from isodual codes over GF(q) of length 2n. Using this method, we find some isodual codes over GF(q), where q=2,3 and 5. In more detail, we obtain binary isodual codes of lengths 32, 34, 36, 38, and 40, where all these codes of lengths 32, 34, and 36 are optimal and some codes of length 38 are optimal. We note that all these binary isodual codes are not self-dual codes, and in particular, in the case of length 38 all their weight enumerators are different from those of binary self-dual codes of the same length; in fact, four binary isodual codes of length 38 are formally self-dual even codes. We construct isodual codes over GF(3) and GF(5) of lengths 4, 6, and 8 as well.

KW - Equivalence

KW - Formally self-dual code

KW - Isodual code

KW - Self-dual code

UR - http://www.scopus.com/inward/record.url?scp=85013212966&partnerID=8YFLogxK

U2 - 10.1016/j.ffa.2017.01.005

DO - 10.1016/j.ffa.2017.01.005

M3 - Article

AN - SCOPUS:85013212966

SN - 1071-5797

VL - 45

SP - 372

EP - 385

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -