Research Article

The weight distribution of hulls of binary codes from incidence matrices of complete graphs

Published in: Quaestiones Mathematicae
Volume 46 , issue 5 , 2023 , pages: 981–992

DOI: 10.2989/16073606.2022.2050434

Author(s): Khumbo Kumwenda Mzuzu University, Malawi , Caleb Namondwe Mzuzu University, Malawi

Keywords: Primary: 05C50 , Secondary: 94B05 , Design , graph , incidence matrix , linear code , weight distribution , weight enumerator

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Abstract

We characterise the weights of all codewords of the hull of the binary code spanned by rows of an incidence matrix B_n of the complete graph K_n for n ≥ 4 and n even. Among others, we show that every codeword of the hull is the sum of an even number of rows of B_n and that its weight depends on the number of rows required to span it. We also determine the weight enumerator and the MacWilliams identity for the hull.

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