Information on Result #1297372
Linear OA(2196, 329, F2, 52) (dual of [329, 133, 53]-code), using construction X with Varšamov bound based on
- linear OA(2192, 324, F2, 52) (dual of [324, 132, 53]-code), using
- 1 times truncation [i] based on linear OA(2193, 325, F2, 53) (dual of [325, 132, 54]-code), using
- concatenation of two codes [i] based on
- linear OA(1632, 65, F16, 26) (dual of [65, 33, 27]-code), using
- extended algebraic-geometric code AGe(F,38P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- extended algebraic-geometric code AGe(F,38P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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(1632, 65, F16, 26) (dual of [65, 33, 27]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2193, 325, F2, 53) (dual of [325, 132, 54]-code), using
- linear OA(2192, 325, F2, 48) (dual of [325, 133, 49]-code), using Gilbert–Varšamov bound and bm = 2192 > Vbs−1(k−1) = 1377 799713 518695 147913 254879 640679 668562 647851 407953 882848 [i]
- linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
- dual of repetition code with length 4 [i]
- caps in base b = 2 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2197, 330, F2, 53) (dual of [330, 133, 54]-code) | [i] | Adding a Parity Check Bit | |