Nonasymptotic Upper Bounds on Binary Single Deletion Codes via Mixed Integer Linear Programming

Valid Linear Programming Bounds for Exact Mixed-Integer Programming

Safe bounds in linear and mixed-integer linear programming

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic,...

Capacity Upper Bounds on Binary Deletion Channels

In this paper, we discuss the problem of bounding the capacity of binary deletion channels in light of the paper, “Tight Asymptotic Bounds for the Deletion Channel with Small Deletion Probabilities” (Kalai, Mitzenmacher, Sudan, 2010), which proves an upper bound of C ≤ 1 − (1 − o(1))H(p) for the capacity of a binary deletion channel for p approaching 0. We present a brief history surrounding th...

Bounds on Mixed Binary/Ternary Codes

Upper and lower bounds are presented for the maximal possible size of mixed binary/ternary error-correcting codes. A table up to length 13 is included. The upper bounds are obtained by applying the linear programming bound to the product of two association schemes. The lower bounds arise from a number of different constructions.

New upper bounds on codes via association schemes and linear programming

Abstract. Let A(n, d) denote the maximum number of codewords in a binary code of length n and minimum Hamming distance d. Upper and lower bounds on A(n, d) have been a subject for extensive research. In this paper we examine upper bounds on A(n, d) as a special case of bounds on the size of subsets in metric association scheme. We will first obtain general bounds on the size of such subsets, ap...