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pro vyhledávání: '"Rifà, Josep"'
In two previous papers we constructed new families of completely regular codes by concatenation methods. Here we determine cases in which the new codes are completely transitive. For these cases we also find the automorphism groups of such codes. For
Externí odkaz:
http://arxiv.org/abs/2303.11190
A subset of a vector space $\mathbb{F}_q^n$ is $K$-additive if it is a linear space over the subfield $K\subseteq \mathbb{F}_q$. Let $q=p^e$, $p$ prime, and $e>1$. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes whic
Externí odkaz:
http://arxiv.org/abs/2001.11609
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t}\times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific
Externí odkaz:
http://arxiv.org/abs/1808.08747
Autor:
Rifà, Josep
We prove that a circulant Hadamard code of length $4n$ can always be seen as an HFP-code (Hadamard full propelinear code) of type $C_{4n}\times C_2$, where $C_2=\langle u\rangle$ or the same, as a cocyclic Hadamard code. We compute the rank and dimen
Externí odkaz:
http://arxiv.org/abs/1711.09373
The ranks and kernels of generalized Hadamard matrices are studied. It is proven that any generalized Hadamard matrix $H(q,\lambda)$ over $F_q$, $q>3$, or $q=3$ and $\gcd(3,\lambda)\not =1$, generates a self-orthogonal code. This result puts a natura
Externí odkaz:
http://arxiv.org/abs/1506.08961
Autor:
del Rio, Ángel, Rifà, Josep
A Z2Z4Q8-code is a non-empty subgroup of a direct product of copies of Z_2, Z_4 and Q_8 (the binary field, the ring of integers modulo 4 and the quaternion group on eight elements, respectively). Such Z2Z4Q8-codes are translation invariant propelinea
Externí odkaz:
http://arxiv.org/abs/1211.5251
Autor:
Rifà, Josep, Zinoviev, Victor
We give a new simple construction for known binary quadratic symmetric bent and almost bent functions. In particular, for even number of variables, they are self-dual and anti-self-dual quadratic bent functions, respectively, which are not of the Mai
Externí odkaz:
http://arxiv.org/abs/1211.5257
We characterize all linear $q$-ary completely regular codes with covering radius $\rho=2$ when the dual codes are antipodal. These completely regular codes are extensions of linear completely regular codes with covering radius 1, which are all classi
Externí odkaz:
http://arxiv.org/abs/1002.4510
Autor:
Rifà, Josep, Zinoviev, Victor
In this paper we consider completely regular codes, obtained from perfect (Hamming) codes by lifting the ground field. More exactly, for a given perfect code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we define a new code C_
Externí odkaz:
http://arxiv.org/abs/1002.0295
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