Counting Constrained Codewords in Binary Linear Codes via Fourier Expansions

Rameshwar, VA and Kashyap, N (2023) Counting Constrained Codewords in Binary Linear Codes via Fourier Expansions. In: 2023 IEEE International Symposium on Information Theory, ISIT 2023, 25 - 30 June 2023, Taipei, pp. 2667-2672.

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Abstract

In this paper, we consider the problem of computing the sizes of subcodes of binary linear codes, all of whose codewords need to satisfy an additional property, which we call a constraint. Using a simple identity from the Fourier analysis of Boolean functions, we transform our counting problem into a question about the structure of the dual code. We illustrate the utility of our method in providing explicit values or numerical algorithms for our counting problem, from the somewhat surprising observation that for different constraints of interest, the Fourier transform of the indicator function of the constraint is efficiently computable. © 2023 IEEE.

Item Type:	Conference Paper
Publication:	IEEE International Symposium on Information Theory - Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to the Institute of Electrical and Electronics Engineers Inc.
Keywords:	Codes (symbols); Computation theory; Fourier transforms; Numerical methods, Binary linear codes; Code-words; Counting problems; Dual codes; Fourier expansion; Fourier's analysis; Numerical algorithms; Property; Simple++; Subcodes, Fourier analysis
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	28 Nov 2023 10:00
Last Modified:	28 Nov 2023 10:00
URI:	https://eprints.iisc.ac.in/id/eprint/83270

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