Bent Vectorial Functions, Codes and Designs

2018/08/26 by Cunsheng Ding, Ding, Cunsheng, Akihiro Munemasa +3 · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1808.08487

openalex publication_date 2018/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (\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.

Cited by

• A Generic Construction of q-ary Near-MDS Codes Supporting 2-Designs with Lengths Beyond q+1

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