It provides an answer in the form of a hierarchy (in larger dimensional spaces) to the question of how to cut Delsarte’s LP polytopes to approximate the true size of linear codes.

Qubit block quantum code that encodes a logical qubit and that is constructed using the Subset-Sum-Linear-Programming (SS-LP) numerical construction. SS-LP codes are optimized to …

Dec 16, 2021 · In this work, we introduce a new hierarchy of linear programs (LPs) that converges to the true size $A^{\text{Lin}}_2(n,d)$ of an optimum linear binary code (in fact, over any finite …

Let G be the generator matrix of the Simplex Code. We have t(G) = 3. Prove this.

Decodes: binary linear codes. turbo codes. “Pseudocodewords:” exact characterization of error patterns causing failure. LP decoding corrects up to errors. Computable efficiently for turbo, …

error detection/correction is easy: The linear codes. 10.1 Basic properties of linear codes De nition 10.1 (Linear codes) A (m;k) code over a eld F is a linear subspace of F m of dimension k.

Bounds on the sizes of codes relative to code word length are invaluable, and one of the strongest such bounds is the linear programming bound developed by Phillipe Delsarte in …

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. …

We can use algebra to design linear codes and to construct efficient encoding and decoding algorithms. The absolute majority of codes designed by coding theorists are linear codes.

We will begin by results on the existence and limitations of codes, both in the Hamming and Shannon approaches. This will highlight some criteria to judge when a code is good, and we …