A matroid Jr' of rank r>.k is k-paving if all of its circuits have cardinality exceeding r-k. In this paper, we develop some basic results concerning k-paving matroids and their connections with codes. Also, we determine all binary 2-paving matroids. (~
On paving matroids and a generalization of MDS codes
β Scribed by Sanjay Rajpal
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 282 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let A be an m\_n matrix in which the entries of each row are all distinct. A. A. Drisko (1998, J. Combin. Theory Ser. A 84, 181 195) showed that if m 2n&1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in the
Dedicated to Professor J. Tits for his sixtieth birthday ABSTRACT. To each arc of PG(n, q) an algebraic hypersurface is associated. Using this tool new results on complete arcs are obtained. Since arcs and linear MDS-codes are equivalent objects, these results can be translated in terms of codes.
We build a class of codes using hermitian forms and the functional trace code. Then we give a general expression of the rth minimum distance of our code and compute general bounds for the weight hierarchy by using exponential sums. We also get the minimum distance and calculate the rth generalized H