Information on Result #708113
Linear OA(4103, 1040, F4, 27) (dual of [1040, 937, 28]-code), using construction XX applied to C1 = C([1021,22]), C2 = C([0,24]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([1021,24]) based on
- linear OA(496, 1023, F4, 25) (dual of [1023, 927, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,22}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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 = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(486, 1023, F4, 23) (dual of [1023, 937, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [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
- linear OA(41, 6, F4, 1) (dual of [6, 5, 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(4103, 952, F4, 2, 27) (dual of [(952, 2), 1801, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4103, 952, F4, 3, 27) (dual of [(952, 3), 2753, 28]-NRT-code) | [i] | ||
| 3 | Digital (76, 103, 952)-net over F4 | [i] | ||
| 4 | Linear OOA(4103, 520, F4, 2, 27) (dual of [(520, 2), 937, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4103, 346, F4, 3, 27) (dual of [(346, 3), 935, 28]-NRT-code) | [i] | ||