Information on Result #686328
Linear OA(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 22]-code), using construction X applied to Ce(20) ⊂ Ce(14) based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(8135, 2097195, F8, 21) (dual of [2097195, 2097060, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8136, 2097196, F8, 21) (dual of [2097196, 2097060, 22]-code) | [i] | ||
| 3 | Linear OA(8137, 2097197, F8, 21) (dual of [2097197, 2097060, 22]-code) | [i] | ||
| 4 | Linear OOA(8134, 2097194, F8, 2, 21) (dual of [(2097194, 2), 4194254, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8134, 2097194, F8, 3, 21) (dual of [(2097194, 3), 6291448, 22]-NRT-code) | [i] | ||
| 6 | Digital (113, 134, 2097194)-net over F8 | [i] | ||
| 7 | Linear OA(8135, 2097196, F8, 21) (dual of [2097196, 2097061, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8136, 2097198, F8, 21) (dual of [2097198, 2097062, 22]-code) | [i] | ||
| 9 | Linear OA(8137, 2097200, F8, 21) (dual of [2097200, 2097063, 22]-code) | [i] | ||
| 10 | Linear OOA(8134, 1048597, F8, 2, 21) (dual of [(1048597, 2), 2097060, 22]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(8134, 699064, F8, 3, 21) (dual of [(699064, 3), 2097058, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(8134, 209719, F8, 21, 21) (dual of [(209719, 21), 4403965, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |