Cyclic arcs and pseudo-cyclic MDS codes
โ Scribed by Tatsuya Maruta
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 294 KB
- Volume
- 174
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
Cyclic arcs (defined by Storme and Van Maldghem, [1994]) and pseudo-cyclic MDS codes are equivalent objects. We survey known results on the existence of cyclic arcs. Some new results on cyclic arcs in PG(2, q) are also given.
๐ SIMILAR VOLUMES
Using maximal arcs in PG(3, 2 m ), we give a new proof of the fact that the binary cyclic code C (m) 1, 2 2h &2 h +1 , the code of length 2 m &1 with defining zeroes : and : t , t=2 2h &2 h +1, where : is a primitive element in GF(2 m ), is 2-error-correcting when gcd(m, h)=1.
In memory of Professor Gian-Carlo Rota for his great contributions in combinatorial and discrete geometry A set of n-tuples over 8 is called a code over 8 or a 8 code if it is a 8 module. A particularly interesting family of 8 -cyclic codes are quadratic residue codes. We define such codes in terms