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Description / Abstract
Error correcting codes (ECC) protect the integrity of a message by detecting and correcting errors that occur in digital communication channels. Cyclic codes are examples of ECC of fixed length n. Cyclic codes of length n are constructed by factoring the polynomial xn+1. In this paper we construct another family of codes by factoring the polynomial xn+xn−1+1. We give the generating and check matrices of these codes and their dimension.
Error correcting codes (ECC) protect the integrity of a message by detecting and correcting errors that occur in digital communication channels. Cyclic codes are examples of ECC of fixed length n. Cyclic codes of length n are constructed by factoring the polynomial xn+1. In this paper we construct another family of codes by factoring the polynomial xn+xn−1+1. We give the generating and check matrices of these codes and their dimension.
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Keywordsdigital, encoder, codewords, computations, Arete the PLNU Honors Journal
Degree AwardedB.S. in Mathematics
Awarding InstitutionPoint Loma Nazarene Unversity
Committee MembersLorinda Carter, Catherine Crockett
Supervisor or ChairJesus Jimenez
Peer Reviewed?No
Collections With This Resource
PLNU Undergraduate Honors Projects
118 Resources
- English
This collection includes projects completed by Point Loma Nazarene University undergraduate honors scholars. These projects are completed under the supervision of a faculty advisor or committee and cover a wide variety of disciplines.