Information on Result #687159
Linear OA(8153, 4100, F8, 44) (dual of [4100, 3947, 45]-code), using construction X applied to Ce(43) ⊂ Ce(42) based on
- linear OA(8153, 4096, F8, 44) (dual of [4096, 3943, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(8149, 4096, F8, 43) (dual of [4096, 3947, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-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(8153, 4100, F8, 2, 44) (dual of [(4100, 2), 8047, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8153, 4100, F8, 3, 44) (dual of [(4100, 3), 12147, 45]-NRT-code) | [i] | ||
| 3 | Digital (109, 153, 4100)-net over F8 | [i] | ||
| 4 | Linear OA(8154, 4192, F8, 44) (dual of [4192, 4038, 45]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(8155, 4369, F8, 44) (dual of [4369, 4214, 45]-code) | [i] | ||
| 6 | Linear OOA(8153, 2050, F8, 2, 44) (dual of [(2050, 2), 3947, 45]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8153, 1366, F8, 3, 44) (dual of [(1366, 3), 3945, 45]-NRT-code) | [i] | ||