90 research outputs found
Further Results on Homogeneous Two-Weight Codes
The results of [1,2] on linear homogeneous two-weight codes over finite
Frobenius rings are exended in two ways: It is shown that certain
non-projective two-weight codes give rise to strongly regular graphs in the way
described in [1,2]. Secondly, these codes are used to define a dual two-weight
code and strongly regular graph similar to the classical case of projective
linear two-weight codes over finite fields [3].Comment: 7 pages, reprinted from the conference proceedings of the Fifth
International Workshop on Optimal Codes and Related Topics (OC2007
Beyond Countable Alphabets: An Extension of the Information-Spectrum Approach
A general approach is established for deriving one-shot performance bounds
for information-theoretic problems on general alphabets beyond countable
alphabets. It is mainly based on the quantization idea and a novel form of
"likelihood ratio". As an example, one-shot lower and upper bounds for random
number generation from correlated sources on general alphabets are derived.Comment: v0.5.1.20be8d, 7 page
Johnson type bounds for mixed dimension subspace codes
Subspace codes, i.e., sets of subspaces of , are applied in
random linear network coding. Here we give improved upper bounds for their
cardinalities based on the Johnson bound for constant dimension codes.Comment: 16 pages, typos correcte
Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Distance 4
It is shown that the maximum size of a binary subspace code of packet length
, minimum subspace distance , and constant dimension is ;
in Finite Geometry terms, the maximum number of planes in
mutually intersecting in at most a point is .
Optimal binary subspace codes are classified into
isomorphism types, and a computer-free construction of one isomorphism type is
provided. The construction uses both geometry and finite fields theory and
generalizes to any , yielding a new family of -ary
subspace codes
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