TY - JOUR
T1 - Bent Vectorial Functions, Codes and Designs
AU - Ding, Cunsheng
AU - Munemasa, Akihiro
AU - Tonchev, Vladimir D.
N1 - Funding Information:
C. Ding was supported by the Hong Kong Research Grants Council under Grant 16300418. V. D. Tonchev was supported in part by the Fulbright Grant.
Funding Information:
Manuscript received August 25, 2018; revised April 24, 2019; accepted May 5, 2019. Date of publication June 13, 2019; date of current version October 18, 2019. C. Ding was supported by the Hong Kong Research Grants Council under Grant 16300418. V. D. Tonchev was supported in part by the Fulbright Grant.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/11
Y1 - 2019/11
N2 - Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group ( ${\mathrm {GF}}(2^{2m}), $ +), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold 2-designs. A new coding-theoretic characterization of bent vectorial functions is presented.
AB - Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group ( ${\mathrm {GF}}(2^{2m}), $ +), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold 2-designs. A new coding-theoretic characterization of bent vectorial functions is presented.
KW - 2-design
KW - Bent function
KW - bent vectorial function
KW - linear code
UR - http://www.scopus.com/inward/record.url?scp=85070554733&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85070554733&partnerID=8YFLogxK
U2 - 10.1109/TIT.2019.2922401
DO - 10.1109/TIT.2019.2922401
M3 - Article
AN - SCOPUS:85070554733
SN - 0018-9448
VL - 65
SP - 7533
EP - 7541
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 11
M1 - 8736398
ER -