Information on Result #1308296
Linear OA(4139, 1047, F4, 37) (dual of [1047, 908, 38]-code), using 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) based on linear OA(4138, 1035, F4, 37) (dual of [1035, 897, 38]-code), using
- construction XX applied to C1 = C([311,345]), C2 = C([309,343]), C3 = C1 + C2 = C([311,343]), and C∩ = C1 ∩ C2 = C([309,345]) [i] based on
- linear OA(4131, 1023, F4, 35) (dual of [1023, 892, 36]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {311,312,…,345}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(4131, 1023, F4, 35) (dual of [1023, 892, 36]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {309,310,…,343}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(4136, 1023, F4, 37) (dual of [1023, 887, 38]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {309,310,…,345}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4126, 1023, F4, 33) (dual of [1023, 897, 34]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {311,312,…,343}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code) (see above)
Mode: 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(4139, 1047, F4, 2, 37) (dual of [(1047, 2), 1955, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4139, 1047, F4, 3, 37) (dual of [(1047, 3), 3002, 38]-NRT-code) | [i] | ||
| 3 | Digital (102, 139, 1047)-net over F4 | [i] | ||