Information on Result #707093
Linear OA(4184, 263, F4, 88) (dual of [263, 79, 89]-code), using construction XX applied to C1 = C([254,85]), C2 = C([0,86]), C3 = C1 + C2 = C([0,85]), and C∩ = C1 ∩ C2 = C([254,86]) based on
- linear OA(4180, 255, F4, 87) (dual of [255, 75, 88]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,85}, and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(4180, 255, F4, 87) (dual of [255, 75, 88]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,86], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(4184, 255, F4, 88) (dual of [255, 71, 89]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,86}, and designed minimum distance d ≥ |I|+1 = 89 [i]
- linear OA(4176, 255, F4, 86) (dual of [255, 79, 87]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,85], and designed minimum distance d ≥ |I|+1 = 87 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code) (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 OA(4192, 281, F4, 88) (dual of [281, 89, 89]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(4189, 271, F4, 88) (dual of [271, 82, 89]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(4184, 131, F4, 2, 88) (dual of [(131, 2), 78, 89]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4184, 87, F4, 3, 88) (dual of [(87, 3), 77, 89]-NRT-code) | [i] | ||