Skew polycyclic codes over the chain ring R^t are the left ideals of the quotient skew polynomial ring, with explicit structural descriptions and generators provided for central f(x) of the form x^{np^s} - lambda when n=1 or 2, plus complete listings for n=1 t=3 and n=2 t=2 that correct prior gaps.
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Constacyclic codes over F_{p^m}[u]/(u^t) of length np^s have explicit ideal generators, with complete enumeration of types, torsional degrees, and cardinalities given for n=1,2,3 and t=3.
The authors obtain generators for ideals in the polycyclic code ring over F_{p^m}[u]/(u^t) and compute cardinalities of the codes for t=4 via torsional degrees.
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Skew Polycyclic Codes over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}$
Skew polycyclic codes over the chain ring R^t are the left ideals of the quotient skew polynomial ring, with explicit structural descriptions and generators provided for central f(x) of the form x^{np^s} - lambda when n=1 or 2, plus complete listings for n=1 t=3 and n=2 t=2 that correct prior gaps.
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Constacyclic codes of length $np^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t\rangle}$: Torsions and Cardinalities
Constacyclic codes over F_{p^m}[u]/(u^t) of length np^s have explicit ideal generators, with complete enumeration of types, torsional degrees, and cardinalities given for n=1,2,3 and t=3.
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On Polycyclic Codes over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}$ and their Cardinalities
The authors obtain generators for ideals in the polycyclic code ring over F_{p^m}[u]/(u^t) and compute cardinalities of the codes for t=4 via torsional degrees.