Information on Result #1315464
Linear OA(32105, 1213, F32, 49) (dual of [1213, 1108, 50]-code), using 175 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 1, 6 times 0, 1, 14 times 0, 1, 28 times 0, 1, 48 times 0, 1, 69 times 0) based on linear OA(3294, 1027, F32, 49) (dual of [1027, 933, 50]-code), using
- construction XX applied to C1 = C([1022,46]), C2 = C([0,47]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([1022,47]) [i] based on
- linear OA(3292, 1023, F32, 48) (dual of [1023, 931, 49]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,46}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3292, 1023, F32, 48) (dual of [1023, 931, 49]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3294, 1023, F32, 49) (dual of [1023, 929, 50]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,47}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3290, 1023, F32, 47) (dual of [1023, 933, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [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(32105, 1213, F32, 2, 49) (dual of [(1213, 2), 2321, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (56, 105, 1213)-net over F32 | [i] | ||
| 3 | Linear OOA(32105, 606, F32, 2, 49) (dual of [(606, 2), 1107, 50]-NRT-code) | [i] | OOA Folding | |