Information on Result #709578
Linear OA(4235, 1045, F4, 62) (dual of [1045, 810, 63]-code), using construction XX applied to C1 = C([1019,56]), C2 = C([0,57]), C3 = C1 + C2 = C([0,56]), and C∩ = C1 ∩ C2 = C([1019,57]) based on
- linear OA(4226, 1023, F4, 61) (dual of [1023, 797, 62]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,56}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,57], and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(4231, 1023, F4, 62) (dual of [1023, 792, 63]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,57}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(4211, 1023, F4, 57) (dual of [1023, 812, 58]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,56], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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(4235, 522, F4, 2, 62) (dual of [(522, 2), 809, 63]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4235, 348, F4, 3, 62) (dual of [(348, 3), 809, 63]-NRT-code) | [i] | ||