Information on Result #1315104
Linear OA(3215, 2765, F32, 6) (dual of [2765, 2750, 7]-code), using 1734 step Varšamov–Edel lengthening with (ri) = (2, 28 times 0, 1, 394 times 0, 1, 1309 times 0) based on linear OA(3211, 1027, F32, 6) (dual of [1027, 1016, 7]-code), using
- construction XX applied to C1 = C([1022,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([1022,4]) [i] based on
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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(3215, 2765, F32, 2, 6) (dual of [(2765, 2), 5515, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (9, 15, 2765)-net over F32 | [i] | ||
| 3 | Linear OOA(3215, 1382, F32, 2, 6) (dual of [(1382, 2), 2749, 7]-NRT-code) | [i] | OOA Folding | |