Information on Result #1297563
Linear OA(2241, 289, F2, 90) (dual of [289, 48, 91]-code), using construction X with Varšamov bound based on
- linear OA(2225, 272, F2, 90) (dual of [272, 47, 91]-code), using
- construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) [i] based on
- linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,84}, and designed minimum distance d ≥ |I|+1 = 90 [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(2219, 255, F2, 91) (dual of [255, 36, 92]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,86}, and designed minimum distance d ≥ |I|+1 = 92 [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(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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
- construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) [i] based on
- linear OA(2225, 273, F2, 74) (dual of [273, 48, 75]-code), using Gilbert–Varšamov bound and bm = 2225 > Vbs−1(k−1) = 43 614880 552852 007608 220667 802881 011875 230416 809678 884925 427900 443124 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
Mode: 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(2241, 289, F2, 89) (dual of [289, 48, 90]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2241, 289, F2, 88) (dual of [289, 48, 89]-code) | [i] | ||
| 3 | Linear OA(2243, 291, F2, 90) (dual of [291, 48, 91]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(2244, 292, F2, 90) (dual of [292, 48, 91]-code) | [i] | ||
| 5 | Linear OA(2245, 293, F2, 90) (dual of [293, 48, 91]-code) | [i] | ||
| 6 | Linear OA(2246, 294, F2, 90) (dual of [294, 48, 91]-code) | [i] | ||
| 7 | Linear OA(2242, 290, F2, 91) (dual of [290, 48, 92]-code) | [i] | Adding a Parity Check Bit | |