Journal ArticleDOI
Perfect Codes in the Lee Metric and the Packing of Polyominoes
Solomon W. Golomb,L. R. Welch +1 more
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This article is published in Siam Journal on Applied Mathematics.The article was published on 1970-03-01. It has received 249 citations till now. The article focuses on the topics: Metric (mathematics) & Hamming bound.read more
Citations
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Journal ArticleDOI
Constructions and properties of Costas arrays
S.W. Golomb,H. Taylor +1 more
TL;DR: A Costas array is an n × n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots.
Proceedings ArticleDOI
Rank modulation for flash memories
TL;DR: A novel data representation scheme for multi-level flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells, is explored.
Journal ArticleDOI
Codes in Permutations and Error Correction for Rank Modulation
Alexander Barg,Arya Mazumdar +1 more
TL;DR: In this paper, the authors derived several lower and upper bounds on the size of codes for rank modulation and showed that for any fixed number of errors, there are codes whose size is within a constant factor of the sphere packing bound.
Journal ArticleDOI
Codes in Permutations and Error Correction for Rank Modulation
Alexander Barg,Arya Mazumdar +1 more
TL;DR: This work derives several lower and upper bounds on the size of codes for rank modulation, and shows the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.
Journal ArticleDOI
Correcting Charge-Constrained Errors in the Rank-Modulation Scheme
TL;DR: Borders on the size of error-correcting codes for charge-constrained errors in the rank-modulation scheme are shown, and metric-embedding techniques are used to give constructions which translate a wealth of knowledge of codes in the Lee metric to codes over permutations in Kendall's ¿-metric.
References
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Journal ArticleDOI
A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Journal ArticleDOI
Rook domains, Latin squares, affine planes, and error-distributing codes
TL;DR: It is shown how various concepts in the theory of Latin squares are best expressed in the form of questions about the placing of rooks on k -dimensional hyperchessboards of side n, and that the optimal colorings in certain cases correspond to duals of desarguian projective planes.