Information on Result #2295761
Linear OA(2222, 270, F2, 83) (dual of [270, 48, 84]-code), using adding a parity check bit based on linear OA(2221, 269, F2, 82) (dual of [269, 48, 83]-code), using
- construction X with Varšamov bound [i] 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, 254, F2, 67) (dual of [254, 48, 68]-code), using Gilbert–Varšamov bound and bm = 2206 > Vbs−1(k−1) = 101 555339 624305 135175 396878 158663 330446 568776 201831 862927 134548 [i]
- linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- linear OA(2206, 253, F2, 82) (dual of [253, 47, 83]-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(2222, 270, F2, 82) (dual of [270, 48, 83]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2222, 270, F2, 81) (dual of [270, 48, 82]-code) | [i] | ||
| 3 | Linear OA(2222, 270, F2, 80) (dual of [270, 48, 81]-code) | [i] | ||
| 4 | Linear OA(2223, 271, F2, 83) (dual of [271, 48, 84]-code) | [i] | Code Embedding in Larger Space | |
| 5 | Linear OA(2220, 268, F2, 81) (dual of [268, 48, 82]-code) | [i] | Truncation | |