Werner Heise, Pasquale Quattrocchi (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Every unit in the ring of the residual classes mod induces canonically an automorphism of the algebra . Let be a cyclic code, i.e. an ideal. If the numbers and are relatively prime then there exists a well-known characterization of the code . We extend this characterization to the general case.
Gashkov, Igor, Larsson, Henrik (2007)
Serdica Journal of Computing
A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n1 +n2; 2(a1 +a2); n2) ≥ min {M1;M2}+1, if A(n1; 2a1; a1 +b1) = M1 and A(n2; 2b2; a2 +b2) = M2, in particular, A(30; 16; 15) = 16 and A(33; 18; 15) = 11.
Jenson, Richard A. (1982)
International Journal of Mathematics and Mathematical Sciences
Solov'eva, F.I., Los', A.V. (2008)
Sibirskij Matematicheskij Zhurnal
P.G. Becker, J.W. Sander (1995)
Semigroup forum
Ionin, Yury J. (2009)
The Electronic Journal of Combinatorics [electronic only]
B. Heinrich Matzat (1992)
Manuscripta mathematica
Václav Snášel, Jiří Bouchala, Petr Vodstrčil (2016)
Pokroky matematiky, fyziky a astronomie
Dominique Perrin (1977)
Mathematische Zeitschrift
А. D. Keedwell (1976)
Zbornik Radova
Carlos Araujo, Italo Dejter (2014)
Discussiones Mathematicae Graph Theory
A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.
Gilles Lachaud (1984/1985)
Séminaire Bourbaki
Honold, Thomas, Landjev, Ivan (2000)
The Electronic Journal of Combinatorics [electronic only]
Haas, Wolfgang, Halupczok, Immanuel, Schlage-Puchta, Jan-Christoph (2009)
The Electronic Journal of Combinatorics [electronic only]
Haas, Wolfgang (2007)
The Electronic Journal of Combinatorics [electronic only]
Britz, Thomas (2002)
The Electronic Journal of Combinatorics [electronic only]
Yannick Guesnet (2001)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
Yannick Guesnet (2010)
RAIRO - Theoretical Informatics and Applications
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
J. L. Lassez (1975/1976)
Groupe d'étude d'algèbre Groupe d'étude d'algèbre
Paul Camion, Bernard Courteau, André Montpetit (1999)
Annales de l'institut Fourier
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.