Geodesic
On the algebraic structure of polycyclic codes
Filomat, Tome 35 (2021) no. 10, p. 3407

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DOI

In this paper, we are interested in the study of the right polycyclic codes as invariant subspaces of F n q by a fixed operator T R. This approach has helped in one hand to connect them to the ideals of the polynomials ring F q [x]/ f (X), where f (x) is the minimal polynomial of T R. On the other hand, it allows to prove that the dual of a right polycyclic code is invariant by the adjoint operator of T R. Hence, when T R is normal we prove that the dual code of a right polycyclic code is also a right polycyclic code. However, when T R isn't normal the dual code is equivalent to a right polycyclic code. Finally, as in the cyclic case, the BCH-like and Hartmann-Tzeng-like bounds for the right polycyclic codes on Hamming distance are derived
DOI : 10.2298/FIL2110407O
Classification : 11T60
Keywords: Cyclic code, polycyclic code, cyclic operator, invariant subspace, BCH and Hartmann-Tzeng bound 
Hassan Ou-Azzou; Mustapha Najmeddine. On the algebraic structure of polycyclic codes. Filomat, Tome 35 (2021) no. 10, p. 3407 . doi: 10.2298/FIL2110407O
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     title = {On the algebraic structure of polycyclic codes},
     journal = {Filomat},
     pages = {3407 },
     year = {2021},
     volume = {35},
     number = {10},
     doi = {10.2298/FIL2110407O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2110407O/}
}
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