Information on Result #709659
Linear OA(4246, 1046, F4, 65) (dual of [1046, 800, 66]-code), using construction XX applied to C1 = C([1019,58]), C2 = C([0,60]), C3 = C1 + C2 = C([0,58]), and C∩ = C1 ∩ C2 = C([1019,60]) based on
- linear OA(4236, 1023, F4, 63) (dual of [1023, 787, 64]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,58}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(4226, 1023, F4, 61) (dual of [1023, 797, 62]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,60], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(4241, 1023, F4, 65) (dual of [1023, 782, 66]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,60}, and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(4221, 1023, F4, 59) (dual of [1023, 802, 60]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,58], and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), 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, 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(4246, 523, F4, 2, 65) (dual of [(523, 2), 800, 66]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4246, 348, F4, 3, 65) (dual of [(348, 3), 798, 66]-NRT-code) | [i] | ||