Isomorph-free exhaustive generation
Journal of Algorithms
Switching Equivalence Classes of Perfect Codes
Designs, Codes and Cryptography
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
The Steiner quadruple systems of order 16
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs
IEEE Transactions on Information Theory
Every binary (2m-2, 22(m)-2-m, 3) code can be lengthened to form a perfect code of length 2m-1
IEEE Transactions on Information Theory
On the Number of -Perfect Binary Codes: A Lower Bound
IEEE Transactions on Information Theory
Binary perfect and extended perfect codes of lengths 15 and 16 and of ranks 13 and 14
Problems of Information Transmission
The perfect binary one-error-correcting codes of length 15: part II-properties
IEEE Transactions on Information Theory
Classification of binary constant weight codes
IEEE Transactions on Information Theory
Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes
Designs, Codes and Cryptography
| Hi-index | 754.97 |
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 these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1024, 4) codes are also classified; there are 38 408 and 5983 such codes, respectively.