Information on Result #706087
Linear OA(445, 275, F4, 14) (dual of [275, 230, 15]-code), using construction XX applied to C1 = C([251,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([251,9]) based on
- linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,8}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(429, 255, F4, 10) (dual of [255, 226, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(441, 255, F4, 14) (dual of [255, 214, 15]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,9}, and designed minimum distance d ≥ |I|+1 = 15 [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(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
- 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
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(445, 275, F4, 2, 14) (dual of [(275, 2), 505, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(445, 275, F4, 3, 14) (dual of [(275, 3), 780, 15]-NRT-code) | [i] | ||
| 3 | Digital (31, 45, 275)-net over F4 | [i] | ||
| 4 | Linear OOA(445, 137, F4, 2, 14) (dual of [(137, 2), 229, 15]-NRT-code) | [i] | OOA Folding | |