Journal
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
Volume 11, Issue 1, Pages 99-114Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/amc.2017005
Keywords
Cyclic codes; codes over local rings; Gray maps
Funding
- TUBITAK (The Scientific and Technological Research Council of Turkey)
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We study cyclic codes over commutative local Frobenius rings of order 16 and give their binary images under a Gray map which is a generalization of the Gray maps on the rings of order 4. We prove that the binary images of cyclic codes are quasi-cyclic codes of index 4 and give examples of cyclic codes of various lengths constructed from these techniques including new optimal quasi-cyclic codes.
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