reedSolomonCode -- constructs the Reed-Solomon code

Synopsis

Usage:

reedSolomonCode(F,L,k)
Inputs:
- F, a ring,
- L, a list,
- k, an integer,
Outputs:
- an instance of the type EvaluationCode,

Description

Given a field F, a list L of different elements of F, and an integer k, returns the Reed-Solomon code obtained when polynomials of degree less than k are evaluated on the elements of L.

i1 : C=reedSolomonCode(ZZ/31,{1,2,3},3);

i2 : peek C

o2 = EvaluationCode{cache => CacheTable{}                                                    }
                    Points => {{1}, {2}, {3}}
                    Sets => {{1, 2, 3}}
                                                               ZZ 3
                    LinearCode => LinearCode{AmbientModule => (--)                          }
                                                               31
                                                          ZZ
                                             BaseField => --
                                                          31
                                             cache => CacheTable{}
                                             Code => image | 1 1 1 |
                                                           | 1 2 4 |
                                                           | 1 3 9 |
                                             GeneratorMatrix => | 1 1 1 |
                                                                | 1 2 3 |
                                                                | 1 4 9 |
                                             Generators => {{1, 1, 1}, {1, 2, 3}, {1, 4, 9}}
                                             ParityCheckMatrix => 0
                                             ParityCheckRows => {}
                                              2
                    PolynomialSet => {1, t , t }
                                          0   0
                                             3     2
                    VanishingIdeal => ideal(t  - 6t  + 11t  - 6)
                                             0     0      0

Ways to use reedSolomonCode :

reedSolomonCode(Ring,List,ZZ)

For the programmer

The object reedSolomonCode is a method function.