Information on Result #2296463
Linear OA(2230, 278, F2, 86) (dual of [278, 48, 87]-code), using strength reduction based on linear OA(2230, 278, F2, 87) (dual of [278, 48, 88]-code), using
- adding a parity check bit [i] based on linear OA(2229, 277, F2, 86) (dual of [277, 48, 87]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2211, 258, F2, 86) (dual of [258, 47, 87]-code), using
- 1 times truncation [i] based on linear OA(2212, 259, F2, 87) (dual of [259, 47, 88]-code), using
- construction X applied to Ce(86) ⊂ Ce(84) [i] based on
- linear OA(2211, 256, F2, 87) (dual of [256, 45, 88]-code), using an extension Ce(86) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,86], and designed minimum distance d ≥ |I|+1 = 87 [i]
- 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]
- 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
- construction X applied to Ce(86) ⊂ Ce(84) [i] based on
- 1 times truncation [i] based on linear OA(2212, 259, F2, 87) (dual of [259, 47, 88]-code), using
- linear OA(2211, 259, F2, 68) (dual of [259, 48, 69]-code), using Gilbert–Varšamov bound and bm = 2211 > Vbs−1(k−1) = 1288 439491 289880 083651 028009 614516 457982 306386 781906 313688 090836 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(2211, 258, F2, 86) (dual of [258, 47, 87]-code), using
- construction X with Varšamov bound [i] based on
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(2228, 276, F2, 84) (dual of [276, 48, 85]-code) | [i] | Truncation | |
| 2 | Linear OA(2227, 275, F2, 83) (dual of [275, 48, 84]-code) | [i] | ||
| 3 | Linear OA(2224, 272, F2, 80) (dual of [272, 48, 81]-code) | [i] | ||