JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON A GENERALIZED APERIODIC PERFECT MAP
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON A GENERALIZED APERIODIC PERFECT MAP
KIM, SANG-MOK;
  PDF(new window)
 Abstract
An aperiodic perfect map(APM) is an array with the property that every array of certain size, called a window, arises exactly once as a contiguous subarray in the array. In this article, we deal with the generalization of APM in higher dimensional arrays. First, we reframe all known definitions onto the generalized n-dimensional arrays. Next, some elementary known results on arrays are generalized to propositions on n-dimensional arrays. Finally, with some devised integer representations, two constructions of infinite family of n-dimensional APMs are generalized from known 2-dimensional constructions in [7].
 Keywords
de Bruijn sequence;aperiodic perfect map;window property;
 Language
English
 Cited by
 References
1.
N. de Bruijn, A combinatorial problem, Proc. Nederlandse Akademie van Wetenschappen 49 (1946), 758-764

2.
J. Burns and C. Mitchell, Coding Schemes for two-dimensional position sending, Cryptography and Coding III, M. Ganley Ed. London, UK: Oxford Univ. Press, pp.31-61, 1993

3.
I. J. Good, Normally recurring decimals, J. London Math. Soc. 21 (1946), 167169

4.
H. Fredricksen, A survey of full length nonlinear shift register cycle algorithms, SIAM J. Algebraic and Discrete Methods 1 (1980), 107-113 crossref(new window)

5.
G. Hurlbert, C. J. Mitchell, and K. G. Paterson, On the existence of de Bruijn tori with two by two windows, J. Combin. Theory Ser. A 76 (1996), 213-230 crossref(new window)

6.
S. Kanetkar and M. Wagh, On Construction of Matrices with distict submatrices, SIAM J. Algebraic and Discrete Methods 1 (1980), 107-113 crossref(new window)

7.
S. Kim, On the existence of aperiodic perfect maps for 2 by 2 windows, Ars Combin. 65 (2002), 111-120

8.
C. J. Mitchell, Aperiodic and semi-periodic perfect maps, IEEE Trans. Inform. Theory 41 (1995), 88-95 crossref(new window)

9.
K. G. Paterson, New Classes of Perfect Maps I, J. Combin. Theory Ser. A 73 (1996), 302-334 crossref(new window)

10.
K. G. Paterson, New Classes of Perfect Maps II, J. Combin. Theory Ser. A 73 (1996), 335-345 crossref(new window)

11.
D. Rees, Note on a paper by I. J. Good, J. London Math. Soc. 21 (1946), 169-172 crossref(new window)