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2014 | 34 | 1 | 57-74
Tytuł artykułu

Lattice-Like Total Perfect Codes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
34
Numer
1
Strony
57-74
Opis fizyczny
Daty
wydano
2014-02-01
online
2014-02-14
Twórcy
autor
Bibliografia
  • [1] C. Araujo, I.J. Dejter and P. Horak, A generalization of Lee codes, Des. Codes Cryptogr., online version, (21 April 2012). doi:10.1007/s10623-012-9666-6[Crossref]
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  • [3] S.I. Costa, M. Muniz, E. Agustini, and R. Palazzo, Graphs, tessellations, and perfect codes on flat tori, IEEE Trans. Inform. Theory 50 (2004) 2363-2377. doi:10.1109/TIT.2004.834754[Crossref]
  • [4] I.J. Dejter and A.A. Delgado, Perfect domination in rectangular grid graphs, J. Combin. Math. Combin. Comput. 70 (2009) 177-196.
  • [5] I.J. Dejter and O. Serra, Efficient dominating sets in Cayley graphs, Discrete Appl. Math. 119 (2003) 319-328. doi:10.1016/S0166-218X(02)00573-5[WoS][Crossref]
  • [6] I.J. Dejter and P. Weichsel, Twisted perfect dominating subgraphs of hypercubes, Congr. Numer. 94 (1993) 67-78.
  • [7] T. Etzion, Product constructions for perfect Lee Codes, IEEE Trans. Inform. Theory 57 (2011) 7473-7481. doi:10.1109/TIT.2011.2161133[Crossref][WoS]
  • [8] S. Golomb and K.Welch, Perfect codes in Lee metric and the packing of polyominoes, SIAM J. Appl. Math. 18 (1970) 302-317. doi:10.1137/0118025[Crossref]
  • [9] D. Hickerson and S. Stein, Abelian groups and packings by semicrosses, Pacific J. Math. 122 (1986) 96-109. doi:10.1137/0118025[Crossref]
  • [10] P. Horak and B.F. AlBdaiwi, Non-periodic tilings of Rn by crosses, Discrete Comput. Geom. 47 (2012) 1-16. doi:10.1007/s00454-011-9373-5[WoS][Crossref]
  • [11] P. Horak and B.F. AlBdaiwi, Diameter perfect Lee codes, IEEE Trans. Inform. Theory 58 (2012) 5490-5499. doi:10.1109/TIT.2012.2196257[Crossref][WoS]
  • [12] W.F. Klostermeyer and J.L. Goldwasser, Total perfect codes in grid graphs, Bull. Inst. Combin. Appl. 46 (2006) 61-68.
  • [13] J. Kratochvil and M. Kriv´anek, On the computational complexity of codes in graphs, in: Proc. MFCS 1988, LN Comp. Sci. 324 (Springer-Verlag) 396-404. doi:10.1007/BFb0017162[Crossref]
  • [14] E. Molnár, Sui Mosaici dello spazio de dimensione n, Atti Accad. Naz. Lincei, Rend. Cl. Sci.Fis. Mat Nat. 51 (1971) 177-185.
  • [15] M. Schwartz, Quasi-cross lattice tilings with applications to flash memory, IEEE Trans. Inform. Theory 58 (2012) 2397-2405. doi:10.1109/TIT.2011.2176718[WoS][Crossref]
  • [16] S. Stein, Packings of Rn by certain error spheres, IEEE Trans. Inform. Theory 30 (1984) 356-363. doi:10.1109/TIT.1984.1056880[Crossref]
  • [17] S. Stein, Factoring by subsets, Pacific J. Math. 22 (1967) 523-541. doi:10.2140/pjm.1967.22.523[Crossref]
  • [18] S. Szabó, On mosaics consisting of mutidimensional crosses, Acta Math. Acad. Sci. Hung. 38 (1981) 191-203. doi:10.1007/BF01917533[Crossref]
  • [19] P.M. Weichsel, Dominating sets of n-cubes, J. Graph Theory 18 (1994) 479-488. doi:10.1002/jgt.3190180506 [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1715
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