Information on Result #709526
Linear OA(4233, 1058, F4, 60) (dual of [1058, 825, 61]-code), using construction XX applied to C1 = C([1019,52]), C2 = C([0,56]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([1019,56]) based on
- linear OA(4211, 1023, F4, 57) (dual of [1023, 812, 58]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [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(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(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(43, 18, F4, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), 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(4233, 529, F4, 2, 60) (dual of [(529, 2), 825, 61]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4233, 352, F4, 3, 60) (dual of [(352, 3), 823, 61]-NRT-code) | [i] | ||