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Z2-Triple cyclic codes and their duals

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

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Abstract (2. Language): 
A Z2-triple cyclic code of block length (r, s, t) is a binary code of length r + s +1 such that the code is partitioned into three parts of lengths r, s and t such that each part is invariant under the cyclic shifts of the coordinates. Such a code can be viewed as Z2[x]-submodules of 1^ x i^s—i x ^t2—1^, in polynomial representation. In this paper, we determine the structure of these codes. We have obtained the form of the generators for such codes. Further, a minimal generating set for such codes is obtained. Also, we study the structure of the duals of these codes via the generators of the codes.
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REFERENCES

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