Information on Result #1297412
Linear OA(2228, 281, F2, 76) (dual of [281, 53, 77]-code), using construction X with Varšamov bound based on
- linear OA(2202, 249, F2, 78) (dual of [249, 47, 79]-code), using
- 7 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]
- 7 times truncation [i] based on linear OA(2209, 256, F2, 85) (dual of [256, 47, 86]-code), using
- linear OA(2202, 255, F2, 64) (dual of [255, 53, 65]-code), using Gilbert–Varšamov bound and bm = 2202 > Vbs−1(k−1) = 5 309715 115877 127733 622700 269313 310221 199959 544388 414039 225696 [i]
- linear OA(220, 26, F2, 11) (dual of [26, 6, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(220, 27, F2, 11) (dual of [27, 7, 12]-code), using
- residual code [i] based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
- concatenation of two codes [i] based on
- residual code [i] based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(220, 27, F2, 11) (dual of [27, 7, 12]-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(2229, 282, F2, 77) (dual of [282, 53, 78]-code) | [i] | Adding a Parity Check Bit | |