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06/19/2023
Codes and Pseudo-Geometric Designs from the Ternary m-Sequences with Welch-type decimation d=2· 3^(n-1)/2+1
Pseudo-geometric designs are combinatorial designs which share the same ...
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07/15/2022
Infinite families of cyclic and negacyclic codes supporting 3-designs
Interplay between coding theory and combinatorial t-designs has been a h...
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06/30/2022
Some 3-designs and shortened codes from binary cyclic codes with three zeros
Linear codes and t-designs are interactive with each other. It is well k...
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02/18/2022
A class of twisted generalized Reed-Solomon codes
Let 𝔽_q be a finite field of size q and 𝔽_q^* the set of non-zero elemen...
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10/08/2021
An infinite family of antiprimitive cyclic codes supporting Steiner systems S(3,8, 7^m+1)
Coding theory and combinatorial t-designs have close connections and int...
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09/28/2021
An Open Problem on the Bentness of Mesnager's Functions
Let n=2m. In the present paper, we study the binomial Boolean functions ...
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09/19/2021
On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and their Consequences
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass o...
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06/15/2021
The subfield codes and subfield subcodes of a family of MDS codes
Maximum distance separable (MDS) codes are very important in both theory...
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10/19/2020
The Projective General Linear Group PGL_2(GF(2^m)) and Linear Codes of Length 2^m+1
The projective general linear group PGL_2(GF(2^m)) acts as a 3-transitiv...
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08/23/2020
The linear codes of t-designs held in the Reed-Muller and Simplex codes
A fascinating topic of combinatorics is t-designs, which have a very lon...
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07/12/2020
Shortened linear codes from APN and PN functions
Linear codes generated by component functions of perfect nonlinear (PN f...
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07/12/2020
Shortened Linear Codes over Finite Fields
The puncturing and shortening technique are two important approaches to ...
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06/15/2020
Fast algebraic immunity of Boolean functions and LCD codes
Nowadays, the resistance against algebraic attacks and fast algebraic at...
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04/10/2020
A Novel Application of Boolean Functions with High Algebraic Immunity in Minimal Codes
Boolean functions with high algebraic immunity are important cryptograph...
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01/01/2020
An infinite family of linear codes supporting 4-designs
The first linear code supporting a 4-design was the [11, 6, 5] ternary G...
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11/22/2019
Full Characterization of Minimal Linear Codes as Cutting Blocking Sets
In this paper, we first study more in detail the relationship between mi...
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10/18/2019
Infinite families of near MDS codes holding t-designs
An [n, k, n-k+1] linear code is called an MDS code. An [n, k, n-k] linea...
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08/05/2019
Minimal linear codes from characteristic functions
Minimal linear codes have interesting applications in secret sharing sch...
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07/30/2019
Codes, differentially δ-uniform functions and t-designs
Special functions, coding theory and t-designs have close connections an...
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07/30/2019
Linear codes of 2-designs associated with subcodes of the ternary generalized Reed-Muller codes
In this paper, the 3-rank of the incidence matrices of 2-designs support...
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05/21/2019
Codebooks from generalized bent Z_4-valued quadratic forms
Codebooks with small inner-product correlation have application in unita...
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04/05/2019
Infinite families of 3-designs from APN functions
Combinatorial t-designs have nice applications in coding theory, finite ...
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03/15/2019
A class of narrow-sense BCH codes over F_q of length q^m-1/2
BCH codes with efficient encoding and decoding algorithms have many appl...
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03/01/2019
On the boomerang uniformity of (quadratic) permutations over F_2^n
At Eurocrypt'18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new t...
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01/26/2019
Steiner systems S(2, 4, 3^m-1/2) and 2-designs from ternary linear codes of length 3^m-1/2
Coding theory and t-designs have close connections and interesting inter...
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11/19/2018
Cyclic bent functions and their applications in codes, codebooks, designs, MUBs and sequences
Let m be an even positive integer. A Boolean bent function f on m-1× is ...
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11/19/2018
A Note on Two Constructions of Zero-Difference Balanced Functions
Notes on two constructions of zero-difference balanced (ZDB) functions a...
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07/05/2018
On the Menezes-Teske-Weng's conjecture
In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conje...
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01/21/2018