Information on Result #1315211
Linear OA(3250, 1564, F32, 21) (dual of [1564, 1514, 22]-code), using 528 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 11 times 0, 1, 33 times 0, 1, 83 times 0, 1, 161 times 0, 1, 232 times 0) based on linear OA(3241, 1027, F32, 21) (dual of [1027, 986, 22]-code), using
- construction XX applied to C1 = C([1022,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1022,19]) [i] based on
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [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(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(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(3250, 1564, F32, 2, 21) (dual of [(1564, 2), 3078, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (29, 50, 1564)-net over F32 | [i] | ||
| 3 | Linear OOA(3250, 782, F32, 2, 21) (dual of [(782, 2), 1514, 22]-NRT-code) | [i] | OOA Folding | |