Information on Result #1315219
Linear OA(3251, 1296, F32, 22) (dual of [1296, 1245, 23]-code), using 261 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 10 times 0, 1, 31 times 0, 1, 73 times 0, 1, 140 times 0) based on linear OA(3243, 1027, F32, 22) (dual of [1027, 984, 23]-code), using
- construction XX applied to C1 = C([1022,19]), C2 = C([0,20]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([1022,20]) [i] based on
- linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-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(3251, 1296, F32, 2, 22) (dual of [(1296, 2), 2541, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (29, 51, 1296)-net over F32 | [i] | ||
| 3 | Linear OOA(3251, 648, F32, 2, 22) (dual of [(648, 2), 1245, 23]-NRT-code) | [i] | OOA Folding | |