Abstract
We consider quasi-cyclic codes over the ring \(\mathbb{F }_2+u\mathbb{F }_2+v\mathbb{F }_2+uv\mathbb{F }_2\), a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.
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Notes
A code with these parameters is also constructed as an index 2 QC code above.
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The authors would like to thank the anonymous referees for their valuable remarks and suggestions that improved the presentation of this paper.
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The first author’s visit was partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK), Grant Number: 1059B211100236.
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Aydin, N., Karadeniz, S. & Yildiz, B. Some new binary quasi-cyclic codes from codes over the ring \(\mathbb F _2+u\mathbb F _2+v\mathbb F _2+uv\mathbb F _2\) . AAECC 24, 355–367 (2013). https://doi.org/10.1007/s00200-013-0207-y
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DOI: https://doi.org/10.1007/s00200-013-0207-y