Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Pottonen, Olli"'
Publikováno v:
Adv. Math. Commun. 10(2) 2016, 393-399
Ternary constant weight codes of length $n=2^m$, weight $n-1$, cardinality $2^n$ and distance $5$ are known to exist for every $m$ for which there exists an APN permutation of order $2^m$, that is, at least for all odd $m \geq 3$ and for $m=6$. We sh
Externí odkaz:
http://arxiv.org/abs/1408.6927
The metric dimension of a graph $G$ is the size of a smallest subset $L \subseteq V(G)$ such that for any $x,y \in V(G)$ with $x\not= y$ there is a $z \in L$ such that the graph distance between $x$ and $z$ differs from the graph distance between $y$
Externí odkaz:
http://arxiv.org/abs/1107.2256
Publikováno v:
IEEE Trans. Inf. Theory 57(10) 2011, 6771-6779
Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^m-4$ and $2^m-3$, respectively) are optimal. Properties of such codes are here studied, determining amon
Externí odkaz:
http://arxiv.org/abs/1104.4013
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification, IEEE Trans.
Externí odkaz:
http://arxiv.org/abs/0909.2526
Publikováno v:
IEEE Trans. Inform. Theory vol. 56, pp. 2571-2582, 2010
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary one-error-correcting codes of
Externí odkaz:
http://arxiv.org/abs/0903.2749
Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
Publikováno v:
IEEE Trans. Inform. Theory 55 (2009) 2622-2625
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect binary on
Externí odkaz:
http://arxiv.org/abs/0810.5633
Publikováno v:
IEEE Trans. Inform. Theory 55 (2009), 4657-4660
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient generation of the
Externí odkaz:
http://arxiv.org/abs/0806.2513
Publikováno v:
In Journal of Computer and System Sciences February 2017 83(1):132-158
Publikováno v:
In Discrete Mathematics 2011 311(10):827-834
Publikováno v:
In Journal of Combinatorial Theory, Series A 2006 113(8):1764-1770