The maximum number of minimal codewords in long codes

Details The maximum number of minimal codewords in long codes The maximum number of minimal codewords in long codes

2012-01-29

arxiv.org/abs/1201.6043v2

Computer Science

Information Theory

9 pages, submitted to Discrete Applied Math

Scientific paper

Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs. This problem (in the graphic case) was considered in 1981 by Entringer and Slater who asked if a connected graph with $p$ vertices and $q$ edges can have only slightly more that $2^{q-p}$ cycles. The bounds in this note answer this in the affirmative for all graphs except possibly some that have fewer than $2p+3\log_2(3p)$ edges. We also conclude that an Eulerian (even) graph has at most $2^{q-p}$ cycles unless the graph is a subdivision of a 4-regular graph that is the edge-disjoint union of two Hamiltonian cycles, in which case it may have as many as $2^{q-p}+p$ cycles.

Affiliated with

Also associated with

No associations

Rating

The maximum number of minimal codewords in long codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The maximum number of minimal codewords in long codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The maximum number of minimal codewords in long codes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-379221