Information on Result #708083
Linear OA(4104, 1039, F4, 27) (dual of [1039, 935, 28]-code), using construction XX applied to C1 = C([321,345]), C2 = C([319,342]), C3 = C1 + C2 = C([321,342]), and C∩ = C1 ∩ C2 = C([319,345]) based on
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {321,322,…,345}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 1023, F4, 24) (dual of [1023, 932, 25]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {319,320,…,342}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4101, 1023, F4, 27) (dual of [1023, 922, 28]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {319,320,…,345}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(481, 1023, F4, 22) (dual of [1023, 942, 23]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {321,322,…,342}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 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
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(4104, 1007, F4, 2, 27) (dual of [(1007, 2), 1910, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4104, 1007, F4, 3, 27) (dual of [(1007, 3), 2917, 28]-NRT-code) | [i] | ||
| 3 | Digital (77, 104, 1007)-net over F4 | [i] | ||