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TitleAbelian codes over Galois rings closed under certain permutations
Author(s) T. Kiran, Bikash Sundar Rajan
TextKiran.T and B. Sundar Rajan, Abelian codes over Galois rings closed under certain permutations, IEEE Trans. Inform. Theory, vol. 49, no. 9, Sept 2003.
TypeTechnical Report, Misc
AbstractWe study-length 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 mixed-radix representation of the coordinate positions and ii) shifting the coordinates by positions. A code is-quasi-cyclic ( -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 unit-invariant Abelian codes and those closed under the second as quasi-cyclic Abelian (QCA) codes. Using a generalized discrete Fourier transform (GDFT) defined over an appropriate extension of the Galois
ring, we show that unit-invariant 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 unit-invariant-QCA code is also an unit-invariant-QCA code. Unit-invariant Abelian (hence unit-invariant cyclic) and-QCA codes over Galois field and over the integer residue rings are obtainable as special cases.
Translation No
Refereed No