-A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the minimum distance of a q-ary repeated-root cyclic code C is expressecin terms of the minimum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the largest known number of codewords for their given length and minimum distance. It is further shown that to a q-ary repeated-root cyclic code C of length n = p%, where p is the characteristic of GF(q) and gcd(p,?i) = 1, there corre-. sponds a simple-root cyclic code C of rate and relative minimum distance at least as large as the corresponding values of C, however, of length ii, i.e., shorter by a factor of p'. The relative minimum distance dmin /n of q-ary repeated-root cyclic codes C of rate r 2 R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity. It is further shown that repeated-root cyclic codes cannot be asymptotically better than simple-root cyclic codes.Mar Terms -Cyclic codes, generator polynomial, formal derivative, Hasse derivative.
We achieve significant improvements in several syntax-based machine translation experiments using a string-to-tree variant of multi bottom-up tree transducers. Our new parameterized rule extraction algorithm extracts string-to-tree rules that can be discontiguous and non-minimal in contrast to existing algorithms for the tree-to-tree setting. The obtained models significantly outperform the string-to-tree component of the Moses framework in a large-scale empirical evaluation on several known translation tasks. Our linguistic analysis reveals the remarkable benefits of discontiguous and non-minimal rules.
In syntax-based machine translation, rule selection is the task of choosing the correct target side of a translation rule among rules with the same source side. We define a discriminative rule selection model for systems that have syntactic annotation on the target language side (stringto-tree). This is a new and clean way to integrate soft source syntactic constraints into string-to-tree systems as features of the rule selection model. We release our implementation as part of Moses.
In this paper, we present the annotation challenges we have encountered when working on a historical language that was undergoing elaboration processes. We especially focus on syntactic ambiguity and gradience in Middle Low German, which causes uncertainty to some extent. Since current annotation tools consider construction contexts and the dynamics of the grammaticalization only partially, we plan to extend CorA -a web-based annotation tool for historical and other nonstandard language data -to capture elaboration phenomena and annotator unsureness. Moreover, we seek to interactively learn morphological as well as syntactic annotations.
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