Information on Result #1315419
Linear OA(3294, 1118, F32, 44) (dual of [1118, 1024, 45]-code), using 81 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 1, 4 times 0, 1, 10 times 0, 1, 21 times 0, 1, 39 times 0) based on linear OA(3284, 1027, F32, 44) (dual of [1027, 943, 45]-code), using
- construction XX applied to C1 = C([1022,41]), C2 = C([0,42]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([1022,42]) [i] based on
- 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(3282, 1023, F32, 43) (dual of [1023, 941, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3284, 1023, F32, 44) (dual of [1023, 939, 45]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,42}, and designed minimum distance d ≥ |I|+1 = 45 [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(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, 1118, F32, 2, 44) (dual of [(1118, 2), 2142, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (50, 94, 1118)-net over F32 | [i] | ||
| 3 | Linear OOA(3294, 559, F32, 2, 44) (dual of [(559, 2), 1024, 45]-NRT-code) | [i] | OOA Folding | |