A New Construction of Nonlinear Codes via Rational Function Fields

It is well known that constructing codes with good parameters one of the most important and fundamental problems in coding theory. Though a great many have been produced, them are defined over alphabets sizes equal to prime powers. In this article, we provide new explicit construction $(q+1)$ -ary nonlinear via rational function fields, where notation="LaTeX">$q$ power. Our constructed by evaluations functions at all places (including place “infinity”) field. Compared algebraic geometry codes, main difference allow be evaluated pole places. After evaluating from union Riemann-Roch spaces, obtain family length notation="LaTeX">$q+1$ alphabet notation="LaTeX">$\mathbb {F}_{q}\cup \{\infty \}$ . As result, our reasonable as they rather close Singleton bound. Furthermore, better than those obtained MDS code restriction or extension. Amazingly, an efficient decoding algorithm can provided for codes.