Information on Result #1315242
Linear OA(3256, 1123, F32, 25) (dual of [1123, 1067, 26]-code), using 89 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 8 times 0, 1, 23 times 0, 1, 52 times 0) based on linear OA(3249, 1027, F32, 25) (dual of [1027, 978, 26]-code), using
- construction XX applied to C1 = C([1022,22]), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([1022,23]) [i] based on
- linear OA(3247, 1023, F32, 24) (dual of [1023, 976, 25]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3247, 1023, F32, 24) (dual of [1023, 976, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3245, 1023, F32, 23) (dual of [1023, 978, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [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(3256, 1123, F32, 2, 25) (dual of [(1123, 2), 2190, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (31, 56, 1123)-net over F32 | [i] | ||
| 3 | Linear OOA(3256, 561, F32, 2, 25) (dual of [(561, 2), 1066, 26]-NRT-code) | [i] | OOA Folding | |