Information on Result #706140
Linear OA(447, 269, F4, 15) (dual of [269, 222, 16]-code), using construction XX applied to C1 = C([253,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([253,12]) based on
- linear OA(441, 255, F4, 13) (dual of [255, 214, 14]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(445, 255, F4, 15) (dual of [255, 210, 16]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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 OOA(447, 246, F4, 2, 15) (dual of [(246, 2), 445, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(447, 246, F4, 3, 15) (dual of [(246, 3), 691, 16]-NRT-code) | [i] | ||
| 3 | Digital (32, 47, 246)-net over F4 | [i] | ||
| 4 | Linear OA(448, 271, F4, 15) (dual of [271, 223, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(447, 134, F4, 2, 15) (dual of [(134, 2), 221, 16]-NRT-code) | [i] | OOA Folding | |