Information on Result #1297219
Linear OA(2116, 146, F2, 44) (dual of [146, 30, 45]-code), using construction X with Varšamov bound based on
- linear OA(2106, 135, F2, 44) (dual of [135, 29, 45]-code), using
- 1 times truncation [i] based on linear OA(2107, 136, F2, 45) (dual of [136, 29, 46]-code), using
- construction X applied to Ce(46) ⊂ Ce(42) [i] based on
- linear OA(2106, 128, F2, 47) (dual of [128, 22, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(299, 128, F2, 43) (dual of [128, 29, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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(46) ⊂ Ce(42) [i] based on
- 1 times truncation [i] based on linear OA(2107, 136, F2, 45) (dual of [136, 29, 46]-code), using
- linear OA(2106, 136, F2, 34) (dual of [136, 30, 35]-code), using Gilbert–Varšamov bound and bm = 2106 > Vbs−1(k−1) = 47 028939 624964 578773 016369 965664 [i]
- linear OA(29, 10, F2, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
- dual of repetition code with length 10 [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2117, 147, F2, 45) (dual of [147, 30, 46]-code) | [i] | Adding a Parity Check Bit | |