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Easily decoded error correcting codes

Smith, R. J. G. (1978) Easily decoded error correcting codes. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.94665) (KAR id:94665)


This thesis is concerned with the decoding aspect of linear block error-correcting codes. When, as in most practical situations, the decoder cost is limited an optimum code may be inferior in performance to a longer sub-optimum code' of the same rate. This consideration is a central theme of the thesis.

The best methods available for decoding short optimum codes and long B.C.H. codes are discussed, in some cases new decoding algorithms for the codes are introduced.

Hashim's "Nested" codes are then analysed. The method of nesting codes which was given by Hashim is shown to be optimum - but it is seen that the codes are less easily decoded than was previously thought.

"Conjoined" codes are introduced. It is shown how two codes with identical numbers of information bits may be "conjoined" to give a code with length and minimum distance equal to the sum of the respective parameters of the constituent codes but with the same number of information bits. A very simple decoding algorithm is given for the codes whereby each constituent codeword is decoded and then a decision is made as to the correct decoding. A technique is given for adding more codewords to conjoined codes without unduly increasing the decoder complexity.

Lastly, "Array" codes are described. They are formed by making parity checks over carefully chosen patterns of information bits arranged in a two-dimensional array. Various methods are given for choosing suitable patterns. Some of the resulting codes are self-orthogonal and certain of these have parameters close to the optimum for such codes. A method is given for adding more codewords to array codes, derived from a process of augmentation known for product codes.

Item Type: Thesis (Doctor of Philosophy (PhD))
DOI/Identification number: 10.22024/UniKent/01.02.94665
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 25 April 2022 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives ( licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies ( If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at and we will seriously consider your claim under the terms of our Take-Down Policy (
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 14 Jul 2023 14:58 UTC
Last Modified: 14 Jul 2023 14:58 UTC
Resource URI: (The current URI for this page, for reference purposes)

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