Information on Result #686331
Linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
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 OA(8114, 2097195, F8, 18) (dual of [2097195, 2097081, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8115, 2097196, F8, 18) (dual of [2097196, 2097081, 19]-code) | [i] | ||
| 3 | Linear OA(8116, 2097197, F8, 18) (dual of [2097197, 2097081, 19]-code) | [i] | ||
| 4 | Linear OOA(8113, 2037364, F8, 2, 18) (dual of [(2037364, 2), 4074615, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8113, 2037364, F8, 3, 18) (dual of [(2037364, 3), 6111979, 19]-NRT-code) | [i] | ||
| 6 | Digital (95, 113, 2037364)-net over F8 | [i] | ||
| 7 | Linear OA(8114, 2097196, F8, 18) (dual of [2097196, 2097082, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8115, 2097198, F8, 18) (dual of [2097198, 2097083, 19]-code) | [i] | ||
| 9 | Linear OA(8116, 2097200, F8, 18) (dual of [2097200, 2097084, 19]-code) | [i] | ||
| 10 | Linear OOA(8113, 1048597, F8, 2, 18) (dual of [(1048597, 2), 2097081, 19]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8113, 699064, F8, 3, 18) (dual of [(699064, 3), 2097079, 19]-NRT-code) | [i] | ||
| 12 | Linear OOA(8113, 233021, F8, 18, 18) (dual of [(233021, 18), 4194265, 19]-NRT-code) | [i] | OA Folding and Stacking | |