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Artículos, Encontrados 8 registros
Artículos Encontrados 8 registros  
1.
13 p, 516.1 KB Rank and kernel of additive generalised Hadamard codes / 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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2.
15 p, 455.1 KB Quaternary group ring codes : ranks, kernels and self-dual codes / Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ; Ten-Valls, Roger (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ; Yildiz, Bahattin (Northern Arizona University. Department of Mathematics and Statistics)
We study G-codes over the ring Z4, which are codes that are held invariant by the action of an arbitrary group G. We view these codes as ideals in a group ring and we study the rank and kernel of these codes. [...]
2020 - 10.3934/amc.2020023
Advances in mathematics of communications, Vol. 14, issue 2 (May 2020) , p. 319-332  
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3.
19 p, 415.1 KB On Z2Z4-additive complementary dual codes and related LCD codes / Benbelkacem, N. (University of Science and Technology Houari Boumediene. Faculty of Mathematics) ; Borges, J. (Joaquim), (Joaquim), dir. (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ; Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. [...]
2020 - 10.1016/j.ffa.2019.101622
Finite Fields and their Applications, Vol. 62 (Feb. 2020) , art. 101622  
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4.
13 p, 1.6 MB Quasi-cyclic codes as cyclic codes over a family of local rings / Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ; Ten-Valls, Roger (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. [...]
2016 - 10.1016/j.ffa.2016.04.002
Finite fields and their applications, Vol. 40 (July 2016) , p. 138-149  
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5.
22 p, 1.2 MB Kernels and ranks of cyclic and negacyclic quaternary codes / Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
We study the rank and kernel of Z4 cyclic codes of odd length n and give bounds on the size of the kernel and the rank. Given that a cyclic code of odd length is of the form C = <fh, 2fg> , where fgh = x^n − 1, we show that <2f> ⊆ K(C) ⊆ C and C ⊆ R(C) ⊆ <fh, 2g> where K(C) is the preimage of the binary kernel and R(C) is the preimage of the space generated by the image of C. [...]
2016 - 10.1007/s10623-015-0163-6
Designs, codes and cryptography, Vol. 81, Issue 2 (Nov. 2016) , p. 347-364  
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6.
8 p, 1010.8 KB Ranks and kernels of codes from generalized Hadamard matrices / 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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7.
22 p, 782.7 KB Z₂Z₄-additive formally self-dual codes / Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
We study odd and even Z₂Z₄ formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence theorems are given for codes of each type defined in the paper.
2014 - 10.1007/s10623-012-9773-4
Designs, codes and cryptography, Vol. 72 Issue 2 (August 2014) , p. 435-453  
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8.
24 p, 1.1 MB Self-dual codes from 3-class association schemes / Bilal, Muhammad (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) ; Dougherty, Steven T. (University of Scranton. Department of Mathematics) ; Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
3-class association schemes are used to construct binary self-dual codes. We use the pure and bordered construction to get self-dual codes starting from the adjacency matrices of symmetric and non-symmetric 3-class association schemes. [...]
2015 - 10.1007/s00200-014-0238-z
Applicable Algebra in Engineering, Communication and Computing, Vol. 26 Issue 3 (June 2015) , p. 227-250  
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1 Dougherty, S. T.
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