Information on Result #709212
Linear OA(4210, 1060, F4, 54) (dual of [1060, 850, 55]-code), using construction XX applied to C1 = C([1019,45]), C2 = C([0,49]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([1019,49]) based on
- linear OA(4186, 1023, F4, 50) (dual of [1023, 837, 51]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,45}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4186, 1023, F4, 50) (dual of [1023, 837, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4201, 1023, F4, 54) (dual of [1023, 822, 55]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,49}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [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(4210, 530, F4, 2, 54) (dual of [(530, 2), 850, 55]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4210, 353, F4, 3, 54) (dual of [(353, 3), 849, 55]-NRT-code) | [i] | ||