Cyclic Codes Over\mathbb{Z}_{4} of Even Length |
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| Authors: | Steven T Dougherty San Ling |
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| Institution: | (1) Department of Mathematics, University of Scranton, Scranton, PA 18510, USA;(2) Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Block 5, Level 3, 1 Nanyang Walk, Singapore, 637616, Republic of Singapore |
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| Abstract: | We determine the structure of cyclic codes over
for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a
given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the
number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less
than or equal to 14.
San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and
DSTA R-394-000-011-422. |
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| Keywords: | cyclic codes codes over rings |
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