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The trace description of irreducible quasi-cyclic codes

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2 Author(s)
G. E. Seguin ; Dept. of Electr. & Comput. Eng., R. Military College, Kingston, Ont., Canada ; G. Drolet

The notion of a q-ary irreducible quasi-cyclic code of block length n and index r is introduced. A trace description of such a code is provided in a fashion similar to the trace description of irreducible cyclic codes. In particular, it is shown that an irreducible quasi-cyclic code of dimension k is completely described by an irreducible cyclic code and r elements from a field of cardinality qk. Using this fact, a number of binary irreducible quasi-cyclic codes of index 2 are constructed and their weight spectra obtained

Published in:

IEEE Transactions on Information Theory  (Volume:36 ,  Issue: 6 )