Linear codes from weakly regular plateaued functions and their secret sharing schemes

DOI10.1007/s10623-018-0556-4zbMath1421.94098OpenAlexW2893369201WikidataQ129188188 ScholiaQ129188188MaRDI QIDQ1727361

Ahmet Sınak, Ferruh Özbudak, Sihem Mesnager

Publication date: 20 February 2019

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-018-0556-4

zbMATH Keywords

weight distributionbinary linear codessecret sharing schemeslinear \(p\)-ary codesweakly regular plateaued functions

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Authentication, digital signatures and secret sharing (94A62)

Related Items (28)

Several classes of minimal binary linear codes violating the Ashikhmin-Barg bound ⋮ Secret sharing schemes based on the dual of Golay codes ⋮ Minimal linear codes from weakly regular bent functions ⋮ Minimal binary linear codes: a general framework based on bent concatenation ⋮ Three Combinatorial Perspectives on Minimal Codes ⋮ Minimal linear codes constructed from functions ⋮ A group identification protocol with leakage resilience of secret sharing scheme ⋮ Strongly regular graphs arising from non-weakly regular bent functions ⋮ Linear codes with few weights from cyclotomic classes and weakly regular bent functions ⋮ Secondary constructions of (non)weakly regular plateaued functions over finite fields ⋮ Constructions of linear codes with two or three weights from vectorial dual-bent functions ⋮ Construction of minimal linear codes with few weights from weakly regular plateaued functions ⋮ Several classes of linear codes with few weights over finite fields ⋮ Vectorial bent functions and linear codes from quadratic forms ⋮ Minimal linear codes from Maiorana-McFarland functions ⋮ Connection of \(p\)-ary \(t\)-weight linear codes to Ramanujan Cayley graphs with \(t+1\) eigenvalues ⋮ Plateaued functions on finite nonabelian groups ⋮ Further projective binary linear codes derived from two-to-one functions and their duals ⋮ Characterizations and constructions of plateaued functions on finite abelian groups ⋮ Several classes of bent functions over finite fields ⋮ Minimal linear codes from weakly regular plateaued balanced functions ⋮ Linear codes with few weights from weakly regular plateaued functions ⋮ Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions ⋮ Minimal linear codes arising from blocking sets ⋮ Wide minimal binary linear codes from the general Maiorana-Mcfarland class ⋮ Recent results and problems on constructions of linear codes from cryptographic functions ⋮ Characterization of \(p\)-ary functions in terms of association schemes and its applications ⋮ A geometric characterization of minimal codes and their asymptotic performance

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A construction of binary linear codes from Boolean functions
• Linear codes with two or three weights from quadratic bent functions
• Linear codes with few weights from weakly regular bent functions based on a generic construction
• On ``bent functions
• The Magma algebra system. I: The user language
• Minimal linear codes over finite fields
• A construction of bent functions from plateaued functions
• A new class of monomial bent functions
• Results on Characterizations of Plateaued Functions in Arbitrary Characteristic
• Characterizations of Plateaued and Bent Functions in Characteristic $$p$$
• Explicit Criteria for Construction of Plateaued Functions
• Linear Codes With Two or Three Weights From Weakly Regular Bent Functions
• A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing
• How to share a secret
• Decomposing bent functions
• Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes
• Monomial and quadratic bent functions over the finite fields of odd characteristic
• The Minimum Distance of Some Narrow-Sense Primitive BCH Codes
• Minimal vectors in linear codes
• New Binomial Bent Functions Over the Finite Fields of Odd Characteristic
• Explicit Characterizations for Plateaued-ness of p-ary (Vectorial) Functions

This page was built for publication: Linear codes from weakly regular plateaued functions and their secret sharing schemes