Information on Result #705939
Linear OA(454, 83, F4, 25) (dual of [83, 29, 26]-code), using construction XX applied to C1 = C([1,22]), C2 = C([9,25]), C3 = C1 + C2 = C([9,22]), and C∩ = C1 ∩ C2 = C([1,25]) based on
- linear OA(440, 63, F4, 22) (dual of [63, 23, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(437, 63, F4, 17) (dual of [63, 26, 18]-code), using the primitive BCH-code C(I) with length 63 = 43−1, defining interval I = {9,10,…,25}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(443, 63, F4, 25) (dual of [63, 20, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(431, 63, F4, 14) (dual of [63, 32, 15]-code), using the primitive BCH-code C(I) with length 63 = 43−1, defining interval I = {9,10,…,22}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(49, 15, F4, 7) (dual of [15, 6, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(455, 84, F4, 25) (dual of [84, 29, 26]-code) | [i] | Code Embedding in Larger Space | |