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09/21/2023
A quaternary analogue of Tang-Ding codes
In a recent paper, Tang and Ding introduced a class of binary cyclic cod...
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09/04/2023
Federated cINN Clustering for Accurate Clustered Federated Learning
Federated Learning (FL) presents an innovative approach to privacy-prese...
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05/18/2023
A new method for solving the equation x^d+(x+1)^d=b in 𝔽_q^4 where d=q^3+q^2+q-1
In this paper, we give a new method answer to a recent conjecture propos...
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05/15/2023
Characterization of Plotkin-optimal two-weight codes over finite chain rings and related applications
Few-weight codes over finite chain rings are associated with combinatori...
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05/04/2023
Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings
The Galois ring GR(4^Δ) is the residue ring Z_4[x]/(h(x)), where h(x) is...
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03/29/2023
Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances
The purpose of this paper is two-fold. First, we characterize the existe...
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11/30/2022
A family of diameter perfect constant-weight codes from Steiner systems
If S is a transitive metric space, then |C|·|A| ≤ |S| for any distance-d...
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11/21/2022
Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs
Linear codes with small hulls over finite fields have been extensively s...
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11/07/2022
A tight upper bound on the number of non-zero weights of a quasi-cyclic code
Let 𝒞 be a quasi-cyclic code of index l(l≥2). Let G be the subgroup of t...
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11/04/2022
Characterization of optimal binary linear codes with one-dimensional hull
The hull of a linear code over finite fields is the intersection of the ...
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11/01/2022
Constructing MRD codes by switching
MRD codes are maximum codes in the rank-distance metric space on m-by-n ...
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10/21/2022
Cyclic codes from low differentially uniform functions
Cyclic codes have many applications in consumer electronics, communicati...
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10/12/2022
Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5
The purpose of this paper is to solve the two conjectures on the largest...
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07/26/2022
Rank and pairs of Rank and Dimension of Kernel of ℤ_pℤ_p^2-linear codes
A code C is called ℤ_pℤ_p^2-linear if it is the Gray image of a ℤ_pℤ_p^2...
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07/05/2022
Additive complementary dual codes over _4
A linear code is linear complementary dual (LCD) if it meets its dual tr...
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06/28/2022
ℤ_pℤ_p^2-additive cyclic codes: kernel and rank
A code C = Φ(𝒞) is called ℤ_p ℤ_p^2-linear if it's the Gray image of the...
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06/28/2022
Gray Images of Cyclic Codes over ℤ_p^2 and ℤ_pℤ_p^2
In the paper, we firstly study the algebraic structures of ℤ_p ℤ_p^k-add...
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06/10/2022
Improved lower and upper bounds for LCD codes?
Linear complementary dual (LCD) codes are linear codes which intersect t...
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05/31/2022
On the coset graph construction of distance-regular graphs
We show that no more new distance-regular graphs in the tables of the bo...
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05/27/2022
ℤ_pℤ_p^2-linear codes: rank and kernel
A code C is called _p_p^2-linear if it is the Gray image of a _p_p^2-add...
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04/06/2022
Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields
In this paper, several conjectures proposed in [2] are studied, involvin...
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04/06/2022
DeFTA: A Plug-and-Play Decentralized Replacement for FedAvg
Federated learning (FL) is identified as a crucial enabler for large-sca...
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03/30/2022
Self-dual Hadamard bent sequences
A new notion of bent sequence related to Hadamard matrices was introduce...
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03/22/2022
The b-symbol weight distribution of irreducible cyclic codes and related consequences
The b-symbol read channel is motivated by the limitations of the reading...
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12/07/2021
The b-symbol weight hierarchy of the Kasami codes
The symbol-pair read channel was first proposed by Cassuto and Blaum. La...
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11/09/2021
On the structure of 1-generator quasi-polycyclic codes over finite chain rings
Quasi-polycyclic (QP for short) codes over a finite chain ring R are a g...
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10/12/2021
An enumeration of 1-perfect ternary codes
We study codes with parameters of the ternary Hamming (n,3^n-m,3) code, ...
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10/11/2021
On q-ary shortened-1-perfect-like codes
We study codes with parameters of q-ary shortened Hamming codes, i.e., (...
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10/02/2021
Complete b-symbol weight distribution of some irreducible cyclic codes
Recently, b-symbol codes are proposed to protect against b-symbol errors...
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09/28/2021
The q-ary antiprimitive BCH codes
It is well-known that cyclic codes have efficient encoding and decoding ...
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09/28/2021
The connections among Hamming metric, b-symbol metric, and r-th generalized Hamming metric
The r-th generalized Hamming metric and the b-symbol metric are two diff...
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06/14/2021
Self-orthogonal codes over a non-unital ring and combinatorial matrices
There is a local ring E of order 4, without identity for the multiplicat...
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05/17/2021
Designs, permutations, and transitive groups
A notion of t-designs in the symmetric group on n letters was introduced...
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03/07/2021
LCD Codes from tridiagonal Toeplitz matrice
Double Toeplitz (DT) codes are codes with a generator matrix of the form...
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02/18/2021
On isodual double Toeplitz codes
Double Toeplitz (shortly DT) codes are introduced here as a generalizati...
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02/16/2021
Designs in finite metric spaces: a probabilistic approach
A finite metric space is called here distance degree regular if its dist...
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05/21/2020
On the number of frequency hypercubes F^n(4;2,2)
A frequency n-cube F^n(4;2,2) is an n-dimensional 4×⋯× 4 array filled by...
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11/15/2019
Two-weight codes over the integers modulo a prime power
Let p be a prime number. Irreducible cyclic codes of length p^2-1 and di...
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06/29/2019
On the number of resolvable Steiner triple systems of small 3-rank
In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derive...
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05/22/2019
The Steiner triple systems of order 21 with a transversal subdesign TD(3,6)
We prove several structural properties of Steiner triple systems (STS) o...
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11/09/2018
On isodual double polycirculant codes
Double polycirculant codes are introduced here as a generalization of do...
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09/28/2018
A new approach to the Kasami codes of type 2
The dual of the Kasami code of length q^2-1, with q a power of 2, is con...
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08/31/2018
On Z_pZ_p^k-additive codes and their duality
In this paper, two different Gray like maps from Z_p^a × Z_p^k^b to Z_p^...
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07/23/2018
The largest number of weights in cyclic codes
Upper and lower bounds on the largest number of weights in a cyclic code...
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06/19/2018
A new distance-regular graph of diameter 3 on 1024 vertices
The dodecacode is a nonlinear additive quaternary code of length 12. By ...
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06/13/2018
Additive perfect codes in Doob graphs
The Doob graph D(m,n) is the Cartesian product of m>0 copies of the Shri...
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06/08/2018
On self-dual and LCD double circulant and double negacirculant codes over F_q + uF_q
Double circulant codes of length 2n over the semilocal ring R = F_q + uF...
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02/24/2018
Linear codes with few weights over F_2+uF_2
In this paper, we construct an infinite family of five-weight codes from...
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02/01/2018
How many weights can a linear code have?
We study the combinatorial function L(k,q), the maximum number of nonzer...
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01/20/2018
