We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

The MacWilliams Identity for Krawtchouk Association Schemes

FRIEDLANDER, ISOBEL,SOPHIE,AIMEE (2024) The MacWilliams Identity for Krawtchouk Association Schemes. Doctoral thesis, Durham University.

PDF - Accepted Version


The weight distribution of an error correcting code is a crucial statistic in determining its performance. One key tool for relating the weight of a code to that of its dual is the MacWilliams Identity, first developed for the Hamming association scheme. This identity has two forms: one is a functional transformation of the weight enumerators, while the other is a direct relation of the weight distributions via eigenvalues of the association scheme. The functional transformation form can, in particular, be used to derive important moment identities for the weight distribution of codes. In this thesis, we focus initially on extending the functional transformation to codes based on skew-symmetric and Hermitian matrices. A generalised b-algebra and new fundamental homogeneous polynomials are then identified and proven to generate the eigenvalues of a specific subclass of association schemes, Krawtchouk association schemes. Based on the new set of MacWilliams Identities as a functional transform, we derive several moments of the weight distribution for all of these codes.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Keywords:MacWilliams Identity, Krawtchouk Polynomials, Association Schemes, Distance Regular Graphs, Weight Distribution
Faculty and Department:Faculty of Science > Computer Science, Department of
Thesis Date:2024
Copyright:Copyright of this thesis is held by the author
Deposited On:02 Feb 2024 09:29

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter