Title :
On the Minimum Distance Conjecture for Schubert Codes
Author_Institution :
GuangZhou Univ., Guangzhou
Abstract :
In 2000, S. R. Ghorpade and G. Lachaud presented a conjecture on the minimum distance of algebraic geometric codes associated to Schubert varieties. In this correspondence, we use the structure and properties of the exterior algebra to give an elementary proof of this conjecture, and provide a construction of codewords of minimum Hamming weight.
Keywords :
Hamming codes; algebraic codes; Schubert codes; algebraic codes; codewords; exterior algebra; geometric codes; minimum Hamming weight; minimum distance conjecture; Algebra; Codes; Galois fields; Hamming weight; Mathematics; Software engineering; Linear code; Schubert variety; minimum distance; projective space; wedge product;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.911283
