Information on Result #709346
Linear OA(4220, 1060, F4, 57) (dual of [1060, 840, 58]-code), using construction XX applied to C1 = C([1019,48]), C2 = C([0,52]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([1019,52]) based on
- linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4211, 1023, F4, 57) (dual of [1023, 812, 58]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [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(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4220, 530, F4, 2, 57) (dual of [(530, 2), 840, 58]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4220, 353, F4, 3, 57) (dual of [(353, 3), 839, 58]-NRT-code) | [i] | ||