Classification and Construction of Self-Dual Convolutional Codes (Master's thesis defense)

Coding Theory and Cryptography Seminars

17 August, Simran Sunil Tinani, 80 views

Self-dual convolutional codes are codes, for which the set of vectors that are orthogonal to every codeword is exactly the code itself. Our main goal will be to construct such self-dual convolutional codes, using a generalized form of the Building-up construction and one of the Harada-Munemasa construction. These are two of the most popular construction methods for binary self-dual linear block codes, which were used to classify binary self-dual linear block codes.

To meet our goal, we will have a closer look at non-catastrophic convolutional codes and connect them to the self-dual convolutional codes, thereby finding equivalent properties to self-duality. Using these equivalent properties, some groups of self-dual convolutional codes will be classified and the two previously mentioned constructions will be generalized for convolutional codes. Finally, we will see whether these generalized constructions might or might not be viable for classification of binary self-dual convolutional codes.

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