Estimating the Sizes of Error-Correcting Constrained Codes Via Fourier Expansions

In this work, we seek to address the problem of designing large (or “high-rate”) codes for communication or storage, all the codewords in which satisfy a constraint that stems from physical defects of the medium over which information transfer occurs. We lend fresh perspective to this classical problem by using tools from Fourier analysis on the Boolean hypercube – this allows us to study the sizes of constrained subcodes of well-known linear codes and obtain efficiently computable upper bounds on the sizes of constrained codes with a prescribed error-correcting capability.

Reference:

[1] V. A. Rameshwar and N. Kashyap, “Estimating the Sizes of Binary Error-Correcting Constrained Codes,” IEEE Journal on Selected Areas in Information Theory, 2023, doi: 10.1109/JSAIT.2023.3279113.