Information on Result #1315409
Linear OA(3294, 1268, F32, 43) (dual of [1268, 1174, 44]-code), using 229 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 1, 0, 0, 0, 1, 10 times 0, 1, 20 times 0, 1, 38 times 0, 1, 62 times 0, 1, 87 times 0) based on linear OA(3282, 1027, F32, 43) (dual of [1027, 945, 44]-code), using
- construction XX applied to C1 = C([1022,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1022,41]) [i] based on
- 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(3280, 1023, F32, 42) (dual of [1023, 943, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3282, 1023, F32, 43) (dual of [1023, 941, 44]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,41}, and designed minimum distance d ≥ |I|+1 = 44 [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(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(3294, 1268, F32, 2, 43) (dual of [(1268, 2), 2442, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (51, 94, 1268)-net over F32 | [i] | ||
| 3 | Linear OOA(3294, 634, F32, 2, 43) (dual of [(634, 2), 1174, 44]-NRT-code) | [i] | OOA Folding | |