Information on Result #2175213
Linear OA(2240, 287, F2, 93) (dual of [287, 47, 94]-code), using adding a parity check bit based on linear OA(2239, 286, F2, 92) (dual of [286, 47, 93]-code), using
- construction XX applied to C1 = C([247,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([247,86]) [i] based on
- linear OA(2225, 255, F2, 93) (dual of [255, 30, 94]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−8,−7,…,84}, and designed minimum distance d ≥ |I|+1 = 94 [i]
- linear OA(2210, 255, F2, 86) (dual of [255, 45, 87]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,86], and designed minimum distance d ≥ |I|+1 = 87 [i]
- linear OA(2227, 255, F2, 95) (dual of [255, 28, 96]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−8,−7,…,86}, and designed minimum distance d ≥ |I|+1 = 96 [i]
- linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,84], and designed minimum distance d ≥ |I|+1 = 85 [i]
- linear OA(211, 28, F2, 5) (dual of [28, 17, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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 OA(2240, 287, F2, 92) (dual of [287, 47, 93]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2240, 287, F2, 91) (dual of [287, 47, 92]-code) | [i] | ||
| 3 | Linear OA(2240, 287, F2, 90) (dual of [287, 47, 91]-code) | [i] | ||
| 4 | Linear OA(2240, 287, F2, 89) (dual of [287, 47, 90]-code) | [i] | ||
| 5 | Linear OA(2240, 287, F2, 88) (dual of [287, 47, 89]-code) | [i] | ||
| 6 | Linear OA(2236, 283, F2, 89) (dual of [283, 47, 90]-code) | [i] | Truncation | |
| 7 | Linear OA(2235, 282, F2, 88) (dual of [282, 47, 89]-code) | [i] | ||
| 8 | Linear OOA(2240, 41, F2, 7, 93) (dual of [(41, 7), 47, 94]-NRT-code) | [i] | OOA Folding | |