Information on Result #1297495
Linear OA(2215, 386, F2, 54) (dual of [386, 171, 55]-code), using construction X with Varšamov bound based on
- linear OA(2213, 383, F2, 54) (dual of [383, 170, 55]-code), using
- 1 times truncation [i] based on linear OA(2214, 384, F2, 55) (dual of [384, 170, 56]-code), using
- concatenation of two codes [i] based on
- linear OA(3230, 64, F32, 27) (dual of [64, 34, 28]-code), using
- extended algebraic-geometric code AGe(F,36P) [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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
- linear OA(3230, 64, F32, 27) (dual of [64, 34, 28]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2214, 384, F2, 55) (dual of [384, 170, 56]-code), using
- linear OA(2213, 384, F2, 52) (dual of [384, 171, 53]-code), using Gilbert–Varšamov bound and bm = 2213 > Vbs−1(k−1) = 12897 847246 648186 725793 640611 681594 878172 036085 981951 149918 665216 [i]
- linear OA(21, 2, F2, 1) (dual of [2, 1, 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 (see above)
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(2216, 387, F2, 55) (dual of [387, 171, 56]-code) | [i] | Adding a Parity Check Bit | |