Information on Result #686261
Linear OA(8121, 2097167, F8, 20) (dual of [2097167, 2097046, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OOA(8121, 1131430, F8, 2, 20) (dual of [(1131430, 2), 2262739, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8121, 1131430, F8, 3, 20) (dual of [(1131430, 3), 3394169, 21]-NRT-code) | [i] | ||
| 3 | Digital (101, 121, 1131430)-net over F8 | [i] | ||
| 4 | Linear OOA(8121, 1048583, F8, 2, 20) (dual of [(1048583, 2), 2097045, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8121, 699055, F8, 3, 20) (dual of [(699055, 3), 2097044, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(8121, 209716, F8, 20, 20) (dual of [(209716, 20), 4194199, 21]-NRT-code) | [i] | OA Folding and Stacking | |