Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Victor G. L. Neumann"'
Publikováno v:
IEEE Access, Vol 10, Pp 39145-39153 (2022)
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of codes wit
Externí odkaz:
https://doaj.org/article/5dbcd1cc5fe94d7aa9769543ff665998
Publikováno v:
Bulletin of the Brazilian Mathematical Society, New Series. 54
Let $\mathbb{F}_{q^n}$ be a finite field with $q^n$ elements and $r$ be a positive divisor of $q^n-1$. An element $\alpha \in \mathbb{F}_{q^n}^*$ is called $r$-primitive if its multiplicative order is $(q^n-1)/r$. Also, $\alpha \in \mathbb{F}_{q^n}$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e65d59a24c0d9e014abef3e26bf2788c
https://doi.org/10.1007/s00574-023-00341-z
https://doi.org/10.1007/s00574-023-00341-z
Autor:
Hemar Godinho, Victor G. L. Neumann
Publikováno v:
International Journal of Number Theory. 17:2113-2130
In this paper, we consider the Diophantine equation in the title, where [Formula: see text] are distinct odd prime numbers and [Formula: see text] are natural numbers. We present many results given conditions for the existence of integers solutions f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::723a058f0d63067c929d307b596d0ee9
https://doi.org/10.1142/s1793042121500792
https://doi.org/10.1142/s1793042121500792
Autor:
Victor G. L. Neumann, Cícero Carvalho
Publikováno v:
Designs, Codes and Cryptography. 89:301-315
Projective Reed-Muller codes are obtained by evaluating homogeneous polynomials of degree d in $${\mathbb {F}}_q[X_0, \ldots , X_n]$$ on the points of a projective space of dimension n defined over a finite field $${\mathbb {F}}_q$$ . They were intro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::21e51cd67d0bd5f9c3a8e07c65f3f00d
https://doi.org/10.1007/s10623-020-00821-z
https://doi.org/10.1007/s10623-020-00821-z
In this paper, we explore the existence of $m$-terms arithmetic progressions in $\mathbb{F}_{q^n}$ with a given common difference whose terms are all primitive elements, and at least one of them is normal. We obtain asymptotic results for $m \ge 4$ a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ffc38a6d23c14c7681ae76ebbe0e211
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of codes wit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd0dd817361f19469b14924f0b7e80c5
In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of $k$-normal elements: an element $\alpha \in \mathbb{F}_{q^n}$ is $k$-normal over $\mathbb{F}_q$ if the greatest common divisor of the polynomials $g_{\alpha}(x)= \alpha x^{n-1}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8ad914292ef16c9a55b645e415754f8
Autor:
Cícero Carvalho, Victor G. L. Neumann
In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class that we defi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d65d5fd68aaab2c82e3b9206b82e61a
Let $$\mathbb {F}_{q^n}$$ be a finite field with $$q^n$$ elements, and let $$m_1$$ and $$m_2$$ be positive integers. Given polynomials $$f_1(x), f_2(x) \in \mathbb {F}_{q^n}[x]$$ with $$\deg (f_i(x)) \le m_i$$ , for $$i = 1, 2$$ , and such that the r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9734f01d473eb2f7f580f9f84b845da
http://arxiv.org/abs/2007.09787
http://arxiv.org/abs/2007.09787
Autor:
Victor G. L. Neumann, Cícero Carvalho
Publikováno v:
Finite Fields and Their Applications. 50:382-390
In this paper we present several values for the next-to-minimal weights of projective Reed–Muller codes. We work over F q with q ≥ 3 since in [3] we have determined the complete values for the next-to-minimal weights of binary projective Reed–M
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4a050ef6ca6d0dd5830363c5cf6a3ed3
https://doi.org/10.1016/j.ffa.2017.12.012
https://doi.org/10.1016/j.ffa.2017.12.012