Information on Result #822544
Linear OOA(423, 518, F4, 2, 6) (dual of [(518, 2), 1013, 7]-NRT-code), using OOA 2-folding based on linear OA(423, 1036, F4, 6) (dual of [1036, 1013, 7]-code), using
- construction XX applied to C1 = C([1022,2]), C2 = C([1,4]), C3 = C1 + C2 = C([1,2]), and C∩ = C1 ∩ C2 = C([1022,4]) [i] based on
- linear OA(416, 1023, F4, 4) (dual of [1023, 1007, 5]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(415, 1023, F4, 4) (dual of [1023, 1008, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(410, 1023, F4, 2) (dual of [1023, 1013, 3]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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(4131, 4194819, F4, 2, 12) (dual of [(4194819, 2), 8389507, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4132, 4194819, F4, 2, 13) (dual of [(4194819, 2), 8389506, 14]-NRT-code) | [i] | ||