Some lower bounds for constant weight codes

New lower bounds for constant weight codes

with M (which is expected). However, as M increases beyond Ahstrart -Some new lower bounds are given for A(n,4, IV), the maximum number of codewords in a binary code of length n, min imum distance 4, and constant weight IV. In a number of cases the results significantly 1.0 improve on the best bounds previously known. h=O 1 .

Upper bounds for constant-weight codes

Let ( ) denote the maximum possible number of codewords in an ( ) constant-weight binary code. We improve upon the best known upper bounds on ( ) in numerous instances for 24 and 12, which is the parameter range of existing tables. Most improvements occur for = 8 10 where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to 28 and 14. To...

Some Lower Bounds for Estrada Index

Some new distance-4 constant weight codes

Improved binary constant weight codes with minimum distance 4 and length at most 28 are constructed. A table with bounds on the chromatic number of small Johnson graphs is given.

On Proving Circuit Lower Bounds Against PH and Some Related Lower Bounds for Constant Depth Circuits

We consider the problem of proving circuit lower bounds against the polynomial-time hierarchy. We give both positive and negative results. For the positive side, for any fixed integer k > 0, we give an explicit Σp2 language, acceptable by a Σ p 2-machine with running time O(n k2+k), that requires circuit size > nk. This provides a constructive version of an existence theorem of Kannan [Kan82]. ...