Information on Result #709006
Linear OA(4186, 1046, F4, 49) (dual of [1046, 860, 50]-code), using construction XX applied to C1 = C([1019,42]), C2 = C([0,44]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([1019,44]) based on
- linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(4166, 1023, F4, 45) (dual of [1023, 857, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4161, 1023, F4, 43) (dual of [1023, 862, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), 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, using
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(4186, 523, F4, 2, 49) (dual of [(523, 2), 860, 50]-NRT-code) | [i] | OOA Folding | |