Title :
New Binary Codes From Rational Function Fields
Author :
Lingfei Jin ; Chaoping Xing
Author_Institution :
Shanghai Key Lab. of Intell. Inf. Process., Fudan Univ., Shanghai, China
Abstract :
In this paper, we present an algebraic construction of binary codes through rational function fields. We make use of certain multiplicative group of rational functions for our construction. In particular, the point at infinity can be employed in our construction to get codes of length up to q+1, where q is the ground field size. As a result, several new binary constant-weight codes are found and many new binary nonlinear codes are presented.
Keywords :
binary codes; nonlinear codes; rational functions; binary constant-weight codes; binary nonlinear codes; multiplicative group; rational function fields; Binary codes; Educational institutions; Electronic mail; Encoding; Lead; Polynomials; Binary codes; binary constant-weight codes; multiplicative group; point at infinity; rational functions;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2014.2352306
