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 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. |
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| Language | English | Volume | 49 | Number | 9 | Year | 2003 | Month | September | Edition | 0 | Translation |
No | Refereed |
No |
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