Results 121 to 130 of about 563,145 (166)

Nilpotent group codes

Journal of Algebra and Its Applications, 2022
In this paper, we consider essential idempotents in the finite semisimple group algebra of a nilpotent group, studying conditions for their existence and other implications. Also, we discuss conditions for nilpotent group codes to be equivalent to Abelian ones.
Duarte, A., Pereira, A., Polcino Milies, C.   +2 more
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GROUP CODES OVER NON-ABELIAN GROUPS

Journal of Algebra and Its Applications, 2013
Let G be a finite group and F a field. We show that all G-codes over F are abelian if the order of G is less than 24, but for F = ℤ5 and G = S4 there exist non-abelian G-codes over F, answering to an open problem posed in [J. J. Bernal, Á. del Río and J. J. Simón, An intrinsical description of group codes, Des.
García Pillado, Cristina, González, Santos, Martínez, Consuelo, Markov, Victor, Nechaev, Alexander   +4 more
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Dual codes of systematic group codes over abelian groups

Applicable Algebra in Engineering, Communication and Computing, 1997
In this paper the class of self-dual codes and dual codes over finite abelian groups are characterized. An \((n,k)\) systematic group code over an abelian group \(G\) is a subgroup of \(G^n\) with order \(|G|^k\) described by \(n-k\) homorphisms \(\Phi_j\), \(j=1,2,\dots,n-k\) of \(G^k\) onto \(G\). Its codewords are \((x_1,\dots,x_k,x_{k+1},\dots,x_n),
Zain, A. A., Sundar Rajan, B.
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Codes from Dihedral 2-Groups

Mathematical Notes, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gupta, S., Rani, P.
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Codes and groups

Journal of Information and Optimization Sciences, 2006
In this paper codes with two control symbols, built over some classes of groups, are studied.
PROCESI, Rita, ROTA R.
openaire   +3 more sources

Group Actions and Codes

Canadian Journal of Mathematics, 2001
AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology .
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Basic Reed–Muller Codes as Group Codes

Journal of Mathematical Sciences, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Automorphism Groups of Convolutional Codes

SIAM Journal on Applied Mathematics, 1978
Let K be the monomial group of degree n, over the field $F = GF( q )$, and let $K^\infty $ denote the group of mappings $x:\mathbb{Z} \to K:i \mapsto x^{( i )} $. For any sequence $v ( D ) = \sum {v_i D^i } $, with $v_i \in F^n $, and any x in $K^\infty $, the x-image of $v( D )$ is defined to be $v( D )x = \sum {v_i x^{( i )} D^i } $.
Delsarte, Ph., Piret, Ph.
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Affine MDS-codes on Groups

Journal of Geometry, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karzel, Helmut, Maxson, Carl J.
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Certain group codes

Proceedings of the IEEE, 1967
Codes are presented for certain combinations of word length n and minimum distance d. Specifically, the codes are for n = 34, d = 13; n = 38, d = 13; n = 28, d = 11; n = 30, d = 11; n = 24, d = 9; n = 26, d = 9. These codes compare favorably with Bose-Chaudhuri codes as regards the number of words.
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