Information on Result #1315397
Linear OA(3292, 1265, F32, 42) (dual of [1265, 1173, 43]-code), using 226 step Varšamov–Edel lengthening with (ri) = (5, 1, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 37 times 0, 1, 62 times 0, 1, 87 times 0) based on linear OA(3280, 1027, F32, 42) (dual of [1027, 947, 43]-code), using
- construction XX applied to C1 = C([1022,39]), C2 = C([0,40]), C3 = C1 + C2 = C([0,39]), and C∩ = C1 ∩ C2 = C([1022,40]) [i] based on
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,39}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3280, 1023, F32, 42) (dual of [1023, 943, 43]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,40}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [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(3292, 1265, F32, 2, 42) (dual of [(1265, 2), 2438, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (50, 92, 1265)-net over F32 | [i] | ||
| 3 | Linear OOA(3292, 632, F32, 2, 42) (dual of [(632, 2), 1172, 43]-NRT-code) | [i] | OOA Folding | |