Information on Result #1315438
Linear OA(3299, 1194, F32, 46) (dual of [1194, 1095, 47]-code), using 156 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 0, 1, 4 times 0, 1, 12 times 0, 1, 23 times 0, 1, 42 times 0, 1, 66 times 0) based on linear OA(3288, 1027, F32, 46) (dual of [1027, 939, 47]-code), using
- construction XX applied to C1 = C([1022,43]), C2 = C([0,44]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([1022,44]) [i] based on
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,43}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3288, 1023, F32, 46) (dual of [1023, 935, 47]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,44}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3284, 1023, F32, 44) (dual of [1023, 939, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [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(3299, 1194, F32, 2, 46) (dual of [(1194, 2), 2289, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 99, 1194)-net over F32 | [i] | ||
| 3 | Linear OOA(3299, 597, F32, 2, 46) (dual of [(597, 2), 1095, 47]-NRT-code) | [i] | OOA Folding | |