65.37 IsMDSCode

IsMDSCode( C )

IsMDSCode returns true if C is a Maximum Distance Seperable code, or MDS code for short. A linear [n, k, d]-code of length n, dimension k and minimum distance d is an MDS code if k=n-d+1, in other words if C meets the Singleton bound (see UpperBoundSingleton). An unrestricted (n, M, d) code is called MDS if k=n-d+1, with k equal to the largest integer less than or equal to the logarithm of M with base q, the size of the base field of C.

Well known MDS codes include the repetition codes, the whole space codes, the even weight codes (these are the only binary MDS Codes) and the Reed-Solomon codes.

    gap> C1 := ReedSolomonCode( 6, 3 );
    a cyclic [6,4,3]2 Reed-Solomon code over GF(7)
    gap> IsMDSCode( C1 );
    true    # 6-3+1 = 4
    gap> IsMDSCode( QRCode( 23, GF(2) ) );
    false 

Previous Up Top Next
Index