Title :
The Weights in MDS Codes
Author :
Ezerman, Martianus Frederic ; Grassl, Markus ; Solé, Patrick
Author_Institution :
Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
Abstract :
The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code.
Keywords :
codes; MDS code; MDS conjecture; dual code; finite field; maximum distance separable code; Error correction codes; Linear code; Polynomials; Quantum mechanics; Rain; Vectors; Covering radius; MDS codes; quantum codes; weight distribution;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2090246
