Information on Result #709603
Linear OA(4242, 1054, F4, 63) (dual of [1054, 812, 64]-code), using construction XX applied to C1 = C([1019,56]), C2 = C([0,58]), C3 = C1 + C2 = C([0,56]), and C∩ = C1 ∩ C2 = C([1019,58]) 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(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(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(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(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- 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
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(4242, 527, F4, 2, 63) (dual of [(527, 2), 812, 64]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4242, 351, F4, 3, 63) (dual of [(351, 3), 811, 64]-NRT-code) | [i] | ||