The length of an s-increasing sequence of r-tuples
- MathematicsComb. Probab. Comput.
A number of results related to a problem of Po-Shen Loh are proved, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.
Orthogonal Polynomials in Information Theory
- Computer Science
The following lectures are based on the works (Tamm, Communication complexity of sum-type functions, 1991, ; Appl Math Lett 7:39–44, 1994, ; Inf Comput 116(2):162–173, 1995, ; Tamm,…
Reflections about a Single Checksum
- Computer ScienceWAIFI
A single checksum for codes consisting of n integer components is investigated and if the errors are such that a single component ci is distorted to ci±ei, the analysis leads to equivalent group factorizations.
Group Factorizations and Information Theory
- Computer Science2007 Information Theory and Applications Workshop
Group factorizations occur in the analysis of syndromes of integer codes, several graphs with large girth important for LDPC codes can be constructed using group factorizations, and various cryptosystems are based on them.
Mathematics: What is the best way to lace your shoes?
It is demonstrated mathematically that the shortest lacing is neither 'criss-cross' or 'straight' lacing, but instead is a rarely used and unexpected type of lacing known as 'bowtie' laces.
Combinatorial packings of R3 by certain error spheres
- MathematicsIEEE Trans. Inf. Theory
One of the "error spheres" discussed by Golomb in 1969, his "Stein corner" in three-dimensional Euclidean space R3 is concerned, and sufficiently dense packings are produced to show that they are much denser than the densest lattice packing.