Information on Result #1297445
Linear OA(2234, 284, F2, 82) (dual of [284, 50, 83]-code), using construction X with Varšamov bound based on
- linear OA(2206, 253, F2, 82) (dual of [253, 47, 83]-code), using
- 3 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]
- 3 times truncation [i] based on linear OA(2209, 256, F2, 85) (dual of [256, 47, 86]-code), using
- linear OA(2206, 256, F2, 66) (dual of [256, 50, 67]-code), using Gilbert–Varšamov bound and bm = 2206 > Vbs−1(k−1) = 63 287182 719006 193662 978460 419802 547993 672750 141960 086002 472192 [i]
- linear OA(225, 28, F2, 15) (dual of [28, 3, 16]-code), using
- repeating each code word 4 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 4 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(2235, 285, F2, 83) (dual of [285, 50, 84]-code) | [i] | Adding a Parity Check Bit | |