The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 , or over even degree extensions of Fp. In the latter case the approach is concatenation with a good code for the Hamming metric as outer code and a short code for the Lee metric as a...

In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of edit-distance that are more powerful than size a modulator to specific class. this line research, Bulian and Dawar [Algorithmica, 75 (2016), pp. 363--382] introduced notion elimination distance showed deciding whether given most $k$ any minor-closed class gra...

We give a shorter proof of a slightly weaker version of a theorem fromGuth and Katz (Ann Math 181:155–190, 2015): we prove that if L is a set of L lines in R3 with at most L1/2 lines in any low degree algebraic surface, then the number of r -rich points of L is L(3/2)+εr−2. This result is one of the main ingredients in the proof of the distinct distance estimate in Guth and Katz (2015). With ou...

Detection of discourse structure is crucial in many text-based applications. This paper presents an original framework for describing textual parallelism which allows us to generalize various discourse phenomena and to propose a unique method to recognize them. With this prospect, we discuss several methods in order to identify the most appropriate one for the problem, and evaluate them based o...