Information on Result #709173
Linear OA(4193, 1040, F4, 51) (dual of [1040, 847, 52]-code), using construction XX applied to C1 = C([1021,46]), C2 = C([0,48]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([1021,48]) based on
- linear OA(4186, 1023, F4, 49) (dual of [1023, 837, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,46}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4191, 1023, F4, 51) (dual of [1023, 832, 52]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,48}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
Mode: Constructive and 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(4193, 520, F4, 2, 51) (dual of [(520, 2), 847, 52]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4193, 346, F4, 3, 51) (dual of [(346, 3), 845, 52]-NRT-code) | [i] | ||