Information on Result #1297402
Linear OA(2221, 271, F2, 76) (dual of [271, 50, 77]-code), using construction X with Varšamov bound based on
- linear OA(2200, 247, F2, 76) (dual of [247, 47, 77]-code), using
- 9 times truncation [i] based on linear OA(2209, 256, F2, 85) (dual of [256, 47, 86]-code), using
- an extension Ce(84) of 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]
- 9 times truncation [i] based on linear OA(2209, 256, F2, 85) (dual of [256, 47, 86]-code), using
- linear OA(2200, 250, F2, 64) (dual of [250, 50, 65]-code), using Gilbert–Varšamov bound and bm = 2200 > Vbs−1(k−1) = 1 276078 301342 703888 154877 366880 741846 289906 449506 221104 908560 [i]
- linear OA(218, 21, F2, 11) (dual of [21, 3, 12]-code), using
- repeating each code word 3 times [i] based on linear OA(24, 7, F2, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
- Simplex code S(3,2) [i]
- repeating each code word 3 times [i] based on linear OA(24, 7, F2, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
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(2223, 273, F2, 76) (dual of [273, 50, 77]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2222, 272, F2, 77) (dual of [272, 50, 78]-code) | [i] | Adding a Parity Check Bit | |