Information on Result #1315344
Linear OA(3282, 1261, F32, 37) (dual of [1261, 1179, 38]-code), using 222 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 9 times 0, 1, 17 times 0, 1, 35 times 0, 1, 60 times 0, 1, 90 times 0) based on linear OA(3270, 1027, F32, 37) (dual of [1027, 957, 38]-code), using
- construction XX applied to C1 = C([1022,34]), C2 = C([0,35]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([1022,35]) [i] based on
- linear OA(3268, 1023, F32, 36) (dual of [1023, 955, 37]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3268, 1023, F32, 36) (dual of [1023, 955, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3270, 1023, F32, 37) (dual of [1023, 953, 38]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3266, 1023, F32, 35) (dual of [1023, 957, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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(3282, 1261, F32, 2, 37) (dual of [(1261, 2), 2440, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (45, 82, 1261)-net over F32 | [i] | ||
| 3 | Linear OOA(3282, 630, F32, 2, 37) (dual of [(630, 2), 1178, 38]-NRT-code) | [i] | OOA Folding | |