Information on Result #1315276
Linear OA(3266, 1306, F32, 29) (dual of [1306, 1240, 30]-code), using 270 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 16 times 0, 1, 38 times 0, 1, 77 times 0, 1, 125 times 0) based on linear OA(3257, 1027, F32, 29) (dual of [1027, 970, 30]-code), using
- construction XX applied to C1 = C([1022,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1022,27]) [i] based on
- linear OA(3255, 1023, F32, 28) (dual of [1023, 968, 29]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3255, 1023, F32, 28) (dual of [1023, 968, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3257, 1023, F32, 29) (dual of [1023, 966, 30]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [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(3266, 1306, F32, 2, 29) (dual of [(1306, 2), 2546, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (37, 66, 1306)-net over F32 | [i] | ||
| 3 | Linear OOA(3266, 653, F32, 2, 29) (dual of [(653, 2), 1240, 30]-NRT-code) | [i] | OOA Folding | |