37 citations · 101 across the 7 of their papers we have counts for
7 papers
Non-existence of a ternary constant weight diameter perfect code
Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen
Ternary constant weight codes of length , weight , cardinality and distance are known to exist for every for which there exists an APN permutation of orde…
Complexity of Metric Dimension on Planar Graphs
Josep Diaz, Olli Pottonen, Maria Serna +1
The metric dimension of a graph is the size of a smallest subset such that for any with there is a such that the graph di…
On Optimal Binary One-Error-Correcting Codes of Lengths and
Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen
Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length and , respectively) ar…
Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes
Patric R. J. Östergård, Olli Pottonen
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. Östergård and O. Pottonen, The perfect binary one-error-corr…
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
Patric R. J. Östergård, Olli Pottonen, Kevin T. Phelps
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. Östergård and…
Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
Ivan Yu. Mogilnykh, Patric R. J. Östergård, Olli Pottonen +1
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 cons…
The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
Patric R. J. Östergård, Olli Pottonen
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 perf…