Information on Result #1815365
OA(8127, 1033, S8, 39), using discarding parts of the base based on linear OA(3276, 1033, F32, 39) (dual of [1033, 957, 40]-code), using
- construction XX applied to C1 = C([1020,34]), C2 = C([0,35]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([1020,35]) [i] based on
- linear OA(3272, 1023, F32, 38) (dual of [1023, 951, 39]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−3,−2,…,34}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(3268, 1023, F32, 36) (dual of [1023, 955, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3274, 1023, F32, 39) (dual of [1023, 949, 40]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−3,−2,…,35}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3266, 1023, F32, 35) (dual of [1023, 957, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), 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(8128, 1034, S8, 39) | [i] | Code Embedding in Larger Space | |