Zobrazeno 1 - 10
of 11
pro vyhledávání: '"Sven Polak"'
Autor:
Sander Gribling, Sven Polak
Publikováno v:
Quantum, Vol 8, p 1318 (2024)
A set of $k$ orthonormal bases of $\mathbb C^d$ is called mutually unbiased if $|\langle e,f\rangle |^2 = 1/d$ whenever $e$ and $f$ are basis vectors in distinct bases. A natural question is for which pairs $(d,k)$ there exist $k$ mutually unbiased b
Externí odkaz:
https://doaj.org/article/0a9cae257ba1409f94f6b29781a29f6d
Publikováno v:
Examples and Counterexamples, Vol 2, Iss , Pp 100051- (2022)
A code C⊆{0,1,2}nis said to be trifferent with length n when for any three distinct elements of C there exists a coordinate in which they all differ. Defining T(n)as the maximum cardinality of trifferent codes with length n, T(n)is unknown for n≥
Externí odkaz:
https://doaj.org/article/19090865bce44ba4b061261f4351cd87
Autor:
Alexander Schrijver, Sven Polak
Publikováno v:
Information Processing Letters, 143, 37-40
Information Processing Letters, 143, 37-40. Elsevier
Information Processing Letters, 143, 37-40. Elsevier
We give an independent set of size $367$ in the fifth strong product power of $C_7$, where $C_7$ is the cycle on $7$ vertices. This leads to an improved lower bound on the Shannon capacity of $C_7$: $\Theta(C_7)\geq 367^{1/5} > 3.2578$. The independe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa2ce816586ec7b2462c3c4e5e8a6e20
https://doi.org/10.1016/j.ipl.2018.11.006
https://doi.org/10.1016/j.ipl.2018.11.006
Autor:
Sven Polak
Publikováno v:
IEEE Transactions on Information Theory, 65(1), 28-38. Institute of Electrical and Electronics Engineers Inc.
For nonnegative integers $n,d,w$, let $A(n,d,w)$ be the maximum size of a code $C \subseteq \mathbb{F}_2^n$ with constant weight $w$ and minimum distance at least $d$. We consider two semidefinite programs based on quadruples of code words that yield
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81b9b7fb1eaeb27a14191c979e490c36
https://hdl.handle.net/11245.1/e187a1bf-7c81-45f8-a729-adddaf9c6738
https://hdl.handle.net/11245.1/e187a1bf-7c81-45f8-a729-adddaf9c6738
Publikováno v:
Electronic Notes in Discrete Mathematics, 68, 227-232. Elsevier
Electronic Notes in Discrete Mathematics, 68, 227-232
Electronic Notes in Discrete Mathematics, 68, 227-232
Let n and k be positive integers with n ≥ 2 k . Consider a circle C with n points 1 , … , n in clockwise order. The interlacing graph IG n , k is the graph with vertices corresponding to k-subsets of [n] that do not contain two adjacent points on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7238bea8e27ae898abc45ecb0c2aa4b
https://doi.org/10.1016/j.endm.2018.06.039
https://doi.org/10.1016/j.endm.2018.06.039
Publikováno v:
Designs, Codes, and Cryptography
Designs, Codes and Cryptography, 84, 87-100
Designs, Codes and Cryptography, 84(1-2), 87-100. Springer Netherlands
Designs, Codes and Cryptography, 84, 87-100
Designs, Codes and Cryptography, 84(1-2), 87-100. Springer Netherlands
For nonnegative integers q, n, d, let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::528c247773c52e7f1adba4bec872622a
https://doi.org/10.1007/s10623-016-0216-5
https://doi.org/10.1007/s10623-016-0216-5
Autor:
Sven Polak
Publikováno v:
Discrete Mathematics, 342(9), 2579-2589
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a semidefinite programm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c35b7e1b7666b0baec333a4540fae959
http://arxiv.org/abs/1810.05066
http://arxiv.org/abs/1810.05066
Autor:
Sven Polak
Publikováno v:
Designs, Codes and Cryptography, 86, 861-874
Designs, Codes, and Cryptography, 86(4). Springer Netherlands
Designs, Codes, and Cryptography
Designs, Codes, and Cryptography, 86(4). Springer Netherlands
Designs, Codes, and Cryptography
For $q,n,d \in \mathbb{N}$, let $A_q(n,d)$ be the maximum size of a code $C \subseteq [q]^n$ with minimum distance at least $d$. We give a divisibility argument resulting in the new upper bounds $A_5(8,6) \leq 65$, $A_4(11,8)\leq 60$ and $A_3(16,11)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c5fcb8bf220fe71c5fd7df45923c0bfb
https://ir.cwi.nl/pub/30361
https://ir.cwi.nl/pub/30361
Autor:
Andries E. Brouwer, Sven Polak
Publikováno v:
Designs, Codes, and Cryptography
Designs, Codes and Cryptography, 87, 1881-1895
Designs, Codes and Cryptography, 87, 1881-1895
For $n,d,w \in \mathbb{N}$, let $A(n,d,w)$ denote the maximum size of a binary code of word length $n$, minimum distance $d$ and constant weight $w$. Schrijver recently showed using semidefinite programming that $A(23,8,11)=1288$, and the second auth
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c06262b47c4dc162263384c687b5c1d9
http://arxiv.org/abs/1709.02195
http://arxiv.org/abs/1709.02195
Publikováno v:
Discrete Applied Mathematics, 259, 232-239
Inspired by a famous characterization of perfect graphs due to Lov\'{a}sz, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $\alpha(H) + \omega(H) \geq |V(H)|$. (Here $\alpha$ and $\omega$ denote the stability number
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c0802e369a4d969de274cf90b20f376