In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k...

Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg [14] first gave a breakthrough result in this topic by cleverly considering subcodes of Reed-Solomon codes. Thus, q-ary optimal locally repairable codes from subcodes of Reed-Solomon codes giv...

One of the interesting problems in coding theory is to determine the valuenq(k, d) which denotes the smallest number n such that an [n, k,d]q code existsfor given k, d and q.For k ≤ 5, there are many results for q ≤ 5 and for k = 6, the results areconcentrated in the ternary code ([1],[3]). In this talk, we concentrated in theproblem to find the exact value nq(6, d)....

It has been known since [Zyablov and Pinsker 1982] that a random q-ary code of rate 1 − Hq(ρ) − ε (where 0 < ρ < 1 − 1/q, ε > 0 and Hq(·) is the q-ary entropy function) with high probability is a (ρ, 1/ε)-list decodable code. (That is, every Hamming ball of radius at most ρn has at most 1/ε codewords in it.) In this paper we prove the “converse” result. In particular, we prove that for every 0 ...

A central problem in coding theory is to determine Aq(n, 2e + 1), the maximal cardinality of a q-ary code of length n correcting up to e errors. When e is fixed and n is large, the best upper bound for A(n, 2e+1) (the binary case) is the well-known Johnson bound from 1962. This however simply reduces to the sphere-packing bound if a Steiner system S(e + 1, 2e + 1, n) exists. Despite the fact th...

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we solve two open problems related to them raised in Phys. Rev. Lett. 117, 150401 (2016). We first show that fundamentally bina...

We extend the Action-Oberon language for executing action systems with typebound actions. Type-bound actions combine the concepts of type-bound procedures (methods) and actions, bringing object orientation to action systems. Typebound actions are created at runtime along with the objects of their bound types. They permit the encapsulation of data and code in objects. Allowing an action to have ...

We consider Metropolis Glauber dynamics for sampling proper qcolourings of the n-vertex complete b-ary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is nO(b/ log b) and our lower bound is nΩ(b/q log(b)), where the constants implicit in the O() and Ω() notation do not depend upon n, q or b.

This article considers the problem of scheduling preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An efficient constructive heuristic is developed for solving large-sized problems. A branch-and-bound algorithm that incorporates a lower bound scheme based on the solution of an assignment problem as well as various dominance rules are presented for solving me...

jahanshahloo has suggested a method for the solving linear programming problems with zero-one variables‎. ‎in this paper we formulate fully fuzzy linear programming problems with zero-one variables and a method for solving these problems is presented using the ranking function and also the branch and bound method along with an example is presented.