Information on Result #1815382
OA(8135, 1030, S8, 42), using discarding parts of the base based on linear OA(3281, 1030, F32, 42) (dual of [1030, 949, 43]-code), using
- construction XX applied to C1 = C([1021,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([1021,39]) [i] based on
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3280, 1023, F32, 42) (dual of [1023, 943, 43]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,39}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3274, 1023, F32, 39) (dual of [1023, 949, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive.
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 | OA(8136, 1031, S8, 42) | [i] | Code Embedding in Larger Space | |
| 2 | OOA(8135, 515, S8, 2, 42) | [i] | OOA Folding | |