Information on Result #706306
Linear OA(469, 269, F4, 23) (dual of [269, 200, 24]-code), using construction XX applied to C1 = C([253,18]), C2 = C([0,20]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([253,20]) based on
- linear OA(463, 255, F4, 21) (dual of [255, 192, 22]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(459, 255, F4, 21) (dual of [255, 196, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(467, 255, F4, 23) (dual of [255, 188, 24]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,20}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(455, 255, F4, 19) (dual of [255, 200, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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
- linear OA(41, 5, F4, 1) (dual of [5, 4, 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 (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(470, 271, F4, 23) (dual of [271, 201, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(469, 134, F4, 2, 23) (dual of [(134, 2), 199, 24]-NRT-code) | [i] | OOA Folding | |