Automatic text categorization has become a vital topic in many applications. Imagine for example the automatic classi cation of Internet pages for a search engine database. The traditional 1-of-n output coding for classi cation scheme needs resources increasing linearly with the number of classes. A di erent solution uses an error correcting code, increasing in length with O(log2(n)) only. In t...

Automatic text categorization has become a vital topic in many applications. Imagine for example the automatic classification of Internet pages for a search engine database. The traditional 1-of-n output coding for classification scheme needs resources increasing linearly with the number of classes. A different solution uses an error correcting code, increasing in length with O(log2(n)) only. I...

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Abstract We show that for a fixed $q$ , the number of -ary $t$ -error correcting codes length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ all $t \leq (1 - q^{-1})n 2\sqrt{n \log n}$ where $H_q(n, t) = q^n/ V_q(n,t)$ Hamming bound and $V_q(n,t)$ cardinality radius ball. This proves conjecture Balogh, Treglown, Wagner, who showed result o(n^{1/3} (\log n)^{-2/3})$ .