Information on Result #1315138
Linear OA(3227, 1706, F32, 11) (dual of [1706, 1679, 12]-code), using 673 step Varšamov–Edel lengthening with (ri) = (2, 1, 6 times 0, 1, 43 times 0, 1, 182 times 0, 1, 437 times 0) based on linear OA(3221, 1027, F32, 11) (dual of [1027, 1006, 12]-code), using
- construction XX applied to C1 = C([1022,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1022,9]) [i] based on
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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(3227, 1706, F32, 2, 11) (dual of [(1706, 2), 3385, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (16, 27, 1706)-net over F32 | [i] | ||
| 3 | Linear OOA(3227, 853, F32, 2, 11) (dual of [(853, 2), 1679, 12]-NRT-code) | [i] | OOA Folding | |