Weight Enumerating Function, Number of Full Rank Sub-matrices and Network Coding

Vaddi, MB and Sundar Rajan, B (2019) Weight Enumerating Function, Number of Full Rank Sub-matrices and Network Coding. In: 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 July 2019 - 12 July 2019, Paris, pp. 867-871.

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Abstract

In most of the network coding problems with k messages, the existence of binary network coding solution over {\mathbb{F}-2} depends on the existence of adequate sets of k-dimensional binary vectors such that each set comprises of linearly independent vectors. In a given k×n (n ≥ k) binary matrix, there exist \binom{n}{k} binary sub-matrices of size k×k. Every possible k×k submatrix may be of full rank or singular depending on the columns present in the matrix. In this work, for full rank binary matrix G of size k×n satisfying certain condition on minimum Hamming weight, we establish a relation between the number of full rank sub-matrices of size k×k and the weight enumerating function of the error correcting code with G as the generator matrix. We give an algorithm to compute the number of full rank k×k submatrices.

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 Institute of Electrical and Electronics Engineers Inc.
Keywords:	Codes (symbols); Matrix algebra, Binary matrix; Binary vectors; Coding problems; Enumerating functions; Error correcting code; Generator matrix; Hamming weights; Linearly independents, Network coding
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	19 Dec 2022 07:03
Last Modified:	19 Dec 2022 07:03
URI:	https://eprints.iisc.ac.in/id/eprint/78500

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