Class $$\mathcal{H}$$ , Niho Bent Functions and o-Polynomials

Mesnager, Sihem

doi:10.1007/978-3-319-32595-8_8

Cited by 2 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After the Ding's works ( [10], [11]), a huge papers appear to determine the parameters (n, K, d H (C)) for binary codes constructed by many types of boolean functions (see the survey paper [16]). In this paper we just consider a simple case by taking bent functions and determine the minimum discrepany δ γ (C) for such binary codes C. For bent functions, the interested readers may refer to the book [18] for more details.…”

Section: Construction Of Cn Codes By Boolean Functionsmentioning

confidence: 99%

Optimal Combinatorial Neural Codes with Matched Metric $δ_{r}$: Characterization and Constructions

Zhang¹,

X²,

Feng³

2021

Preprint

View full text Add to dashboard Cite

Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in [6] introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" δ r called asymmetric discrepancy, instead of the Hamming distance d H for usual error-correcting codes. They also presented the Hamming, Singleton and Plotkin bounds for CN codes with respect to δ r and asked how to construct the CN codes C with large size |C| and δ r (C). In this paper we firstly show that a binary code C reaches one of the above bounds for δ r (C) if and only if C reaches the corresponding bounds for d H and r is sufficiently closed to 1. This means that all optimal CN codes come from the usual optimal codes. Secondly we present several constructions of CN codes with nice and flexible parameters (n, K, δ r (C)) by using bent functions.

show abstract

Section: Construction Of Cn Codes By Boolean Functionsmentioning

confidence: 99%

Optimal Combinatorial Neural Codes with Matched Metric $δ_{r}$: Characterization and Constructions

Zhang¹,

X²,

Feng³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…When n = 1, n-to-1 mappings also have useful applications in large areas, especially in cryptography, finite geometry, coding theory and combinatorial design. For example, the well known bent functions, class H can be constructed from 2-to-1 mappings over finite fields with characteristic 2, by Carlet and Mesnager [5,21]. Univariate Niho bent functions were constructed from the well-known o-polynomial, a class of polynomial characterized by 2-to-1 mappings [4].…”

mentioning

confidence: 99%

Characterizations and constructions of n-to-1 mappings over finite fields

Niu¹,

Li²,

Qu³

et al. 2022

Preprint

View full text Add to dashboard Cite

n-to-1 mappings have wide applications in many areas, especially in cryptography, finite geometry, coding theory and combinatorial design. In this paper, many classes of n-to-1 mappings over finite fields are studied. First, we provide a characterization of general n-to-1 mappings over F p m by means of the Walsh transform. Then, we completely determine 3-to-1 polynomials with degree no more than 4 over F p m .

show abstract

Class $$\mathcal{H}$$ , Niho Bent Functions and o-Polynomials

Cited by 2 publications

References 19 publications

Optimal Combinatorial Neural Codes with Matched Metric $δ_{r}$: Characterization and Constructions

Optimal Combinatorial Neural Codes with Matched Metric $δ_{r}$: Characterization and Constructions

Characterizations and constructions of n-to-1 mappings over finite fields

Contact Info

Product

Resources

About