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Affine invariant extended cyclic codes over Galois rings

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2 Author(s)
Dey, B.K. ; Int. Inst. of Inf. Technol., Hyderabad, India ; Rajan, B.S.

Recently, Blackford and Ray-Chaudhuri used transform domain techniques to permutation groups of cyclic codes over Galois rings. They used the same technique to find a set of necessary and sufficient conditions for extended cyclic codes of length 2m over any subring of GR(4,m) to be affine invariant. Here, we use the same technique to find a set of necessary and sufficient conditions for extended cyclic codes of length pm over any subring of GR(pe,m) to be affine invariant, for e=2 with arbitrary p and for p=2 with arbitrary e. These are used to find two new classes of affine invariant Bose-Chaudhuri-Hocquenghem (BCH) and generalized Reed-Muller (GRM) codes over Z2e for arbitrary e and a class of affine invariant BCH codes over Zp2 for arbitrary prime p.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 4 )