Information on Result #706068
Linear OA(435, 269, F4, 11) (dual of [269, 234, 12]-code), using construction XX applied to C1 = C([253,6]), C2 = C([0,8]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([253,8]) based on
- linear OA(429, 255, F4, 9) (dual of [255, 226, 10]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(425, 255, F4, 9) (dual of [255, 230, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(421, 255, F4, 7) (dual of [255, 234, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(435, 254, F4, 2, 11) (dual of [(254, 2), 473, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(435, 254, F4, 3, 11) (dual of [(254, 3), 727, 12]-NRT-code) | [i] | ||
| 3 | Digital (24, 35, 254)-net over F4 | [i] | ||
| 4 | Linear OA(436, 271, F4, 11) (dual of [271, 235, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(435, 134, F4, 2, 11) (dual of [(134, 2), 233, 12]-NRT-code) | [i] | OOA Folding | |