T. Aaron Gulliver
4 papers in the PaperMetrix corpus
Papers by this author
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On Repeated-Root Constacyclic Codes of Length $2^amp^r$ over Finite Fields
2015 · arXiv (Cornell University)
In this paper we investigate the structure of repeated root constacyclic codes of length $2^amp^r$ over $\mathbb{F}_{p^s}$ with $a\geq1$ and $(m,p)=1$. We characterize the codes in terms of their generator polynomials. This provides simple conditions …
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On extremal double circulant self-dual codes of lengths $90$-$96$
2016 · arXiv (Cornell University)
A classification of extremal double circulant self-dual codes of lengths up to $88$ is known. We give a classification of extremal double circulant self-dual codes of lengths $90,92,94$ and $96$. We also classify double circulant …
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An analog of the prime number theorem for finite fields via truncated polylogarithm expansions
2016 · Mathematics of Computation
An exponentially accurate asymptotic expansion of the truncated polylogarithm function is derived that leads to an asymptotic formula for enumerating monic irreducible polynomials over finite fields. This formula is analogous to the asymptotic expansion formula …
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Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences
2025 · Notes on Number Theory and Discrete Mathematics
In this paper, we define two new sequences using the generalized Mersenne numbers, Fibonacci p-numbers, and m-balancing numbers. These sequences are constructed using the Hadamard-type product of their characteristic polynomials. The determinants and combinatorial and …