Information on Result #2181218
Linear OA(2168, 535, F2, 38) (dual of [535, 367, 39]-code), using strength reduction based on linear OA(2168, 535, F2, 39) (dual of [535, 367, 40]-code), using
- construction XX applied to C1 = C([509,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([509,36]) [i] based on
- linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2153, 511, F2, 36) (dual of [511, 358, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2144, 511, F2, 34) (dual of [511, 367, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(24, 14, F2, 2) (dual of [14, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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(2168, 107, F2, 5, 38) (dual of [(107, 5), 367, 39]-NRT-code) | [i] | OOA Folding | |