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Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula… (More)

We consider the problem of enumerating the number of irreducible transformation shift registers. We give an asymptotic formula for the number of irreducible transformation shift registers in some special cases. Moreover, we derive a short proof for the exact number of irreducible transformation shift registers of order two using a recent generalization of a… (More)

We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The case of varieties defined by the vanishing of 2 × 2 minors is considered in some detail. Here we obtain the complete… (More)

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