Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Luis H. Gallardo"'
Autor:
Mireille Car, Luis H. Gallardo
Publikováno v:
Acta Arithmetica. 197:293-309
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c540fe09c50875438a5eb02198d2cb0f
https://doi.org/10.4064/aa200324-30-7
https://doi.org/10.4064/aa200324-30-7
Autor:
Luis H. Gallardo
Publikováno v:
Volume: 28, Issue: 28 1-8
International Electronic Journal of Algebra
International Electronic Journal of Algebra
We prove that there is no perfect binary polynomial $R$ that is the sum of two appropriate powers, besides, possibly $R=P+1$ with $P$ irreducible. The proofs follow from analogue results involving the ABC-theorem for polynomials and a classical ident
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2723d8cabe3f096cf64b8cd2cd19d4d5
https://doi.org/10.24330/ieja.768086
https://doi.org/10.24330/ieja.768086
Autor:
Luis H. Gallardo
Publikováno v:
Mathematical Communications
Volume 26
Issue 1
Volume 26
Issue 1
We prove, under a mild condition, that there is no circulant Hadamard matrix ( H) with (n >4) rows when (sqrt{n/4}) is not square-free. The proof introduces a new method to attack Ryser's Conjecture, that is a long standing difficult conjecture.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______951::2bc1d3ad48e5b0caffa7b52aa1045012
https://hrcak.srce.hr/252594
https://hrcak.srce.hr/252594
Publikováno v:
Finite Fields and Their Applications
Finite Fields and Their Applications, Elsevier, 2019, 59, pp.284-296. ⟨10.1016/j.ffa.2019.06.006⟩
Finite Fields and Their Applications, Elsevier, 2019, 59, pp.284-296. ⟨10.1016/j.ffa.2019.06.006⟩
We work over the field with two elements. We establish a new correspondence between Mersenne polynomials and trinomials so that corresponding polynomials have the same number of irreducible factors. This allows us to get a partial but nontrivial resu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f23793d8d2a17cf43b6e31213f498ea
https://hal.archives-ouvertes.fr/hal-03488314
https://hal.archives-ouvertes.fr/hal-03488314
Autor:
Luis H. Gallardo
Publikováno v:
Mathematical Communications
Volume 24
Issue 2
Volume 24
Issue 2
We prove the nonexistence of a circulant Hadamard matrix H of order n, under technical conditions on the eigenvalues of H, when n has only two odd prime divisors and in the general case
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______951::b1729b663107db500902f607e03aa636
https://hrcak.srce.hr/file/330690
https://hrcak.srce.hr/file/330690
Publikováno v:
Funct. Approx. Comment. Math. 55, no. 1 (2016), 7-21
We complete, in this paper, the characterization of all known even perfect polynomials over the prime field $\mathbb{F}_2$. In particular, we prove that the last two of the eleven known ``sporadic'' perfect polynomials over $\mathbb{F}_2$ are the uni
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a19e90fee6f97cd373706b51c861a11
https://doi.org/10.7169/facm/2016.55.1.1
https://doi.org/10.7169/facm/2016.55.1.1
Autor:
Luis H. Gallardo
Publikováno v:
The Electronic Journal of Combinatorics. 23
We associate to any given circulant complex matrix $C$ another one $E(C)$ such that $E(E(C)) = C^{*}$ the transpose conjugate of $C.$ All circulant Hadamard matrices of order $4$ satisfy a condition $C_4$ on their eigenvalues, namely, the absolute va
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::15c1fa666ceda39e8e83ba025c1705e0
https://doi.org/10.37236/5237
https://doi.org/10.37236/5237
Publikováno v:
Finite Fields and Their Applications. 18:920-932
We give all even perfect (resp. unitary perfect) polynomials over the prime field F 2 of the form x a ( x + 1 ) b M 1 h 1 ⋯ M r h r , where each M i is a Mersenne irreducible polynomial, h i = 2 n i − 1 (resp. h i = 2 n i ) and a , b , r , n i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a2bfb162a5991c2f748e37d0a0f0c761
https://doi.org/10.1016/j.ffa.2012.06.004
https://doi.org/10.1016/j.ffa.2012.06.004
Publikováno v:
Journal of Symbolic Computation. 47:492-502
A polynomial [email protected]?F"2[x] is unitary perfect if and only if [email protected]?d|A,gcd(d,A/d)=1d. We find all unitary perfect polynomials of the form P"1^a^"^1P"2^a^"^2P"3^a^"^3P"4^a^"^4 where P"1,...,P"[email protected]?F"2[x] are irreduc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a74fd6739207994942eff8aa6e2c26d4
https://doi.org/10.1016/j.jsc.2011.09.009
https://doi.org/10.1016/j.jsc.2011.09.009
Publikováno v:
Portugaliae Mathematica. 69:283-303
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cf59e8d7deefa0c7ffd67520e9a4417f
https://doi.org/10.4171/pm/1918
https://doi.org/10.4171/pm/1918