Some results concerning linear codes and (k, 3)-caps in three-dimensional Galois space
- 1 September 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 84 (2) , 191-205
- https://doi.org/10.1017/s0305004100055031
Abstract
The packing problem for (k, 3)-caps is that of finding (m, 3)r, q, the largest size of (k, 3)-cap in the Galois space Sr, q. The problem is tackled by exploiting the interplay of finite geometries with error-correcting codes. An improved general upper bound on (m, 3)3 q and the actual value of (m, 3)3, 4 are obtained. In terms of coding theory, the methods make a useful contribution to the difficult task of establishing the existence or non-existence of linear codes with certain weight distributions.Keywords
This publication has 3 references indexed in Scilit:
- Caps and codesDiscrete Mathematics, 1978
- Some results concerning {(q+1)(n−1);n}-arcs and {(q+1)(n−1)+1;n}-arcs in finite projective planes of order qJournal of Combinatorial Theory, Series A, 1975
- A Theorem on the Distribution of Weights in a Systematic Code†Bell System Technical Journal, 1963