Irreducible Cyclic Codes and Polyadic Codes

In this book, explicit expressions of all thegenerating idempotents of irreducible cyclic codes oflength p^n and 2p^n over GF(q) are obtained, where pis an oddprime, p does not divide (q^f-1)/p if n 1 and f isthe multiplicative order of q modulo p. Also thegenerating idempotents of all theirreducible cyclic codes of length 2^n over GF(q),where q is any odd prime power, are determined.It is also proved that the generating idempotents ofirreducible cyclic codes can be effectivelyevaluated, once they are known for irreducible cycliccodes of length prime power length. The weightdistributions of all the irreducible cyclic codes oflength 2^n are also obtained directly from theirgenerating polynomials. The necessary and sufficientconditions for the existence of cyclic polyadic codesof prime powerlength and of arbitrary length are obtained. The results on the existence of polyadiccodes, obtained by us, will enable one to constructpolyadic codes of varying lengths and dimensions.Many interesting examples of good codes arise fromthe family of polyadic codes.

Autorentext

Dr. Anuradha Sharma presently holds the position of Associate Professor and Co-ordinator in Faculty of Pharmaceutical Sciences, PCTE Group of Institutes, Baddowal, Ludhiana. She has a teaching and research experience of more than 10 years. Her main areas of research include computer aided drug design, synthesis, and study of new chemical entities.