Details:
Title  Abelian codes over Galois rings closed under certain permutations  Author(s)  T. Kiran, Bikash Sundar Rajan  Text  Kiran.T and B. Sundar Rajan, Abelian codes over Galois rings closed under
certain permutations, IEEE Trans. Inform. Theory, vol. 49, no. 9, Sept 2003.  Type  Technical Report, Misc  Abstract  We studylength Abelian codes over Galois rings with characteristic , where and are relatively prime, having the additional structure of being closed under the following two permutations: i)
permutation effected by multiplying the coordinates with a unit in the appropriate mixedradix representation of the coordinate positions and ii) shifting the coordinates by positions. A code isquasicyclic ( QC) if is an integer such that cyclic shift of a codeword by positions gives
another codeword. We call the Abelian codes closed under the first permutation as unitinvariant Abelian codes and those closed under the second as quasicyclic Abelian (QCA) codes. Using a generalized discrete Fourier transform (GDFT) defined over an appropriate extension of the Galois
ring, we show that unitinvariant Abelian and QCA codes can be easily characterized in the transform domain. For =1, QCA codes coincide with those that are cyclic as well as Abelian. The number of such codes for a specified size and length is obtained and we also show that the dual
of an unitinvariantQCA code is also an unitinvariantQCA code. Unitinvariant Abelian (hence unitinvariant cyclic) andQCA codes over Galois field and over the integer residue rings are obtainable as special cases. 
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 Language  English  Volume  49  Number  9  Year  2003  Month  September  Edition  0  Translation 
No  Refereed 
No 
