In these notes, we address bounds for error-correcting codes. Our approach is from the viewpoint of algebraic graph theory. We therefore begin with a review of the algebraic structure of the Hamming graph, focusing on the binary case. We then derive Delsarte’s linear programming bound and explore some applications of it. In the second part of the notes, we introduce Terwilliger’s subconstituent...

Dynamic programming is an algorithm design technique, which allows to improve efficiency by avoiding re-computation of identical subtasks. We present a new recursion combinator, dynamorphism, which captures the dynamic programming recursion pattern with memoization and identify some simple conditions when functions defined by structured general recursion can be redefined as a dynamorphism. The ...

My research explores methods for automatic generation of high-quality feedback for computer programming exercises. This work is motivated by problems with current automated assessment systems, which usually provide binary (“Correct”/“Incorrect”) feedback on programming exercises. Binary feedback is not conducive to student learning, and has also been linked to undesirable consequences, such as ...

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes...

in this paper, an algorithm is presented for the formation of optimal null basis vectors corresponding to sparse flexibility matrices. for controlling the independence of the vectors, a generator is selected in each corresponding self-equilibrating systems, and the sequence of generators is modeled as decision variables. since the equilibrium conditions and uniqueness of generators consists a u...

in this article, a finite horizon, multi product and multi period economic order quantity like seasonal items is considered where demand rate is deterministic and known but variable in each period. the order quantities of items come in batch sizes and the end of the period order quantity and, consequently, demand of customers are zero. in addition, storage space is constrained and the problem ...

We construct examples of contingency tables on n binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide evidence that linear programming may not be an effective heuristic for detecting disclosures when releasing margins of multi-way tables.

The Veri ed Programming Language Implementation project has developed a formally veri ed implementation of the Scheme programming language. This report documents the image builder, which lays out a binary image for a program. It contains detailed proofs that the operational semantics of the resulting output matches the operational semantics of the input.

To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension do...

We apply Schrijver’s semidefinite programming method to obtain improved upper bounds on generalized distances and list decoding radii of binary codes.