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13 p, 516.1 KB |
Rank and kernel of additive generalised Hadamard codes
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Dougherty, Steven T. (University of Scranton. Department of Mathematics) ;
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
A subset of a vector space Fn q is additive if it is a linear space over the field Fp, where q = pe, p prime, and e > 1. Bounds on the rank and dimension of the kernel of additive generalised Hadamard (additive GH) codes are established. [...]
2021 -  10.1109/TIT.2021.3100433
IEEE Transactions on Information Theory, Vol. 67, Issue 11 (November 2021) , p. 7210-7220
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14 p, 129.7 KB |
Completely regular codes with different parameters giving the same distance-regular coset graphs
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Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Zinoviev, Victor (Russian Academy of Sciences (Rússia). Kharkevich Institute for Information Transmission Problems)
We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b}ρ=min{a,b} and identical intersection array, specifically, one code over F_q^r for each divisor r of a or b. [...]
2017 - 10.1016/j.disc.2017.03.001
Discrete Mathematics, Vol. 340 Núm. 7 (July 2017) , p. 1649-1656
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7 p, 234.2 KB |
About non equivalent completely regular codes with identical intersection array
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Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Zinoviev, Victor ((Russian Academy of Sciences (Rússia). Kharkevich Institute for Information Transmission Problems))
We obtain several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a, b, we construct completely transitive codes over different fields with covering radius ρ = min{a, b} and identical intersection array, specifically, we construct one code over F_{q^r} for each divisor r of a or b. [...]
2017 - 10.1016/j.endm.2017.02.030
Electronic notes in discrete mathematics, Vol. 57 (Març 2017) , p. 181-186
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6 p, 1.4 MB |
About some Hadamard full propelinear (2t,2,2)-codes : Rank and Kernel
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Bailera, Ivan (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Borges, J. (Joaquim) (Joaquim) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
A new subclass of Hadamard full propelinear codes is introduced in this article. We define the HFP(2t,2,2)-codes as codes with a group structure isomorphic to C₂t × C₂^2. Concepts such as rank and dimension of the kernel are studied, and bounds for them are established. [...]
2016 - 10.1016/j.endm.2016.09.055
Electronic notes in discrete mathematics, Vol. 54 (Oct. 2016) , p. 319-324
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8 p, 1010.8 KB |
Ranks and kernels of codes from generalized Hadamard matrices
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Dougherty, Steven T. (University of Scranton. Department of Mathematics) ;
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q, λ) over Fq , q > 3, or q = 3 and gcd(3, λ) ≠ 1, generates a self-orthogonal code. [...]
2016 - 10.1109/TIT.2015.2509061
IEEE transactions on information theory, Vol. 62 No. 2 (Feb. 2016) , p. 687-694
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24 p, 809.3 KB |
Self-embeddings of Hamming Steiner triple systems of small order and APN permutations
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Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Solov'eva, Faina I. (Sobolev Institute of Mathematics) ;
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n = 2 m − 1 for small m (m ≤ 22), is given. As far as we know, for m ∈ {5, 7, 11, 13, 17, 19}, all given self-embeddings in closed surfaces are new. [...]
2015 - 10.1007/s10623-013-9909-1
Designs, codes and cryptography, Vol. 75 Issue 3 (June 2015) , p. 405-427
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21 p, 3.7 MB |
Families of nested completely regular codes and distance-regular graphs
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Borges, J. (Joaquim) (Joaquim) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ;
Zinoviev, Victor (Harkevich Institute for Problems of Information Transmission)
In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2 i th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 m − 1 (respectively, 2 m ), where m = 2u. [...]
2015 - 10.3934/amc.2015.9.233
Advances in mathematics of communications, Vol. 9 Issue 2 (May 2015) , p. 233-246
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