Information on Result #706518
Linear OA(4102, 282, F4, 33) (dual of [282, 180, 34]-code), using construction XX applied to C1 = C([251,25]), C2 = C([0,28]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([251,28]) based on
- linear OA(487, 255, F4, 30) (dual of [255, 168, 31]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,25}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(483, 255, F4, 29) (dual of [255, 172, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(495, 255, F4, 33) (dual of [255, 160, 34]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,28}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(475, 255, F4, 26) (dual of [255, 180, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
- linear OA(43, 11, F4, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), 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 OA(4101, 281, F4, 32) (dual of [281, 180, 33]-code) | [i] | Truncation | |
| 2 | Linear OOA(4102, 141, F4, 2, 33) (dual of [(141, 2), 180, 34]-NRT-code) | [i] | OOA Folding | |