Information on Result #906466
Linear OOA(7107, 63, F7, 2, 69) (dual of [(63, 2), 19, 70]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(710, 9, F7, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(710, 13, F7, 2, 9) (dual of [(13, 2), 16, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- discarding factors / shortening the dual code based on linear OOA(710, 13, F7, 2, 9) (dual of [(13, 2), 16, 10]-NRT-code), using
- linear OOA(712, 9, F7, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(712, 13, F7, 2, 11) (dual of [(13, 2), 14, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 12, 13)-net over F7, using
- 1 times m-reduction [i] based on digital (1, 13, 13)-net over F7 (see above)
- extracting embedded OOA [i] based on digital (1, 12, 13)-net over F7, using
- discarding factors / shortening the dual code based on linear OOA(712, 13, F7, 2, 11) (dual of [(13, 2), 14, 12]-NRT-code), using
- linear OOA(714, 9, F7, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 14, 9)-net over F7, using
- net from sequence [i] based on digital (1, 8)-sequence over F7, using
- extracting embedded OOA [i] based on digital (1, 14, 9)-net over F7, using
- linear OOA(717, 9, F7, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
- dual of repetition NRT-code with length 9 [i]
- linear OOA(718, 9, F7, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
- linear OOA(718, 9, F7, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
- linear OOA(718, 9, F7, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7107, 63, F7, 2, 68) (dual of [(63, 2), 19, 69]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(7109, 64, F7, 2, 69) (dual of [(64, 2), 19, 70]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(7105, 62, F7, 2, 67) (dual of [(62, 2), 19, 68]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(7103, 61, F7, 2, 65) (dual of [(61, 2), 19, 66]-NRT-code) | [i] | ||
| 5 | Linear OOA(7101, 60, F7, 2, 63) (dual of [(60, 2), 19, 64]-NRT-code) | [i] | ||