Information on Result #1297443
Linear OA(2230, 279, F2, 82) (dual of [279, 49, 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, 255, F2, 66) (dual of [255, 49, 67]-code), using Gilbert–Varšamov bound and bm = 2206 > Vbs−1(k−1) = 47 279330 379156 015983 347482 362125 377488 620496 789893 822697 429771 [i]
- linear OA(222, 24, F2, 15) (dual of [24, 2, 16]-code), using
- repeating each code word 8 times [i] based on 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
- repeating each code word 8 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), 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(2230, 279, F2, 81) (dual of [279, 49, 82]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2231, 280, F2, 83) (dual of [280, 49, 84]-code) | [i] | Adding a Parity Check Bit | |