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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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12/07/2022
An upper bound on the number of frequency hypercubes
A frequency n-cube F^n(q;l_0,...,l_m-1) is an n-dimensional q-by-...-by-...
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12/07/2022
Multifold 1-perfect codes
A μ-fold (multifold) 1-perfect code in any graph is a set C of vertices ...
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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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11/01/2022
Constructing MRD codes by switching
MRD codes are maximum codes in the rank-distance metric space on m-by-n ...
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06/30/2022
Projective tilings and full-rank perfect codes
A tiling of a finite vector space R is the pair (U,V) of its subsets suc...
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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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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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11/30/2020
[[2,10],[6,6]]-equitable partitions of the 12-cube
We describe the computer-aided classification of equitable partitions of...
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11/30/2020
On minimal subspace Zp-null designs
Let q be a power of a prime p, and let V be an n-dimensional space over ...
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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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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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05/27/2019
On the orthogonal arrays of parameters OA(1536,13,2,7) and related
With a computer-aided approach based on the connection with equitable pa...
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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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03/01/2019
On the number of autotopies of an n-ary qusigroup of order 4
An algebraic system from a finite set Σ of cardinality k and an n-ary op...
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01/31/2019
On two-fold packings of radius-1 balls in Hamming graphs
A λ-fold r-packing in a Hamming metric space is a code C such that the r...
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01/31/2019
On (2n/3-1)-resilient (n,2)-functions
A {00,01,10,11}-valued function on the vertices of the n-cube is called ...
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01/31/2019
On dual codes in the Doob schemes
The Doob scheme D(m,n'+n") is a metric association scheme defined on E_4...
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12/07/2018
On completely regular codes of covering radius 1 in the halved hypercubes
We consider constructions of covering-radius-1 completely regular codes,...
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10/31/2018
On the gaps of the spectrum of volumes of trades
A pair {T_0,T_1} of disjoint collections of k-subsets (blocks) of a set ...
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10/09/2018
The existence of perfect codes in Doob graphs
We solve the problem of existence of perfect codes in the Doob graph. It...
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08/31/2018