Name
Abstract | ||
|---|---|---|
We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have recently been studied. The basic parameters such as the length, dimension and minimum distance of these codes are known only in special cases. An upper bound for the minimum distance is known and it is conjectured that this bound is achieved. We give explicit formulae for the length and dimension of arbitrary Schubert codes and prove the minimum distance conjecture in the affirmative for codes associated to Schubert divisors. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.ffa.2004.09.002 | Finite Fields and Their Applications |
Keywords | Field | DocType |
minimum distance,schubert variety,explicit formula,schubert variety.,grassmannian,arbitrary schubert code,linear codes,algebraic geometry,schubert code,. grassmannian,basic parameter,projective system,difficult question,linear code,minimum distance conjecture,enumerative combinatorics,schubert divisor,upper bound,error correction code,finite field | Discrete mathematics,Hamming code,Combinatorics,Algebra,Block code,Schubert calculus,Expander code,Enumerative combinatorics,Linear code,Schubert variety,Mathematics,Singleton bound | Journal |
Volume | Issue | ISSN |
11 | 4 | Finite Fields and their Applications, Vol. 11, No. 4 (2005), pp.
684-699. |
Citations | PageRank | References |
7 | 0.96 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sudhir R. Ghorpade | 1 | 80 | 12.16 |
| Michael A. Tsfasman | 2 | 25 | 19.34 |