Information on Result #1297326
Linear OA(2169, 320, F2, 42) (dual of [320, 151, 43]-code), using construction X with Varšamov bound based on
- linear OA(2167, 317, F2, 42) (dual of [317, 150, 43]-code), using
- 1 times truncation [i] based on linear OA(2168, 318, F2, 43) (dual of [318, 150, 44]-code), using
- concatenation of two codes [i] based on
- linear OA(3223, 53, F32, 21) (dual of [53, 30, 22]-code), using
- extended algebraic-geometric code AGe(F,31P) [i] based on function field F/F32 with g(F) = 2 and N(F) ≥ 53, 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(3223, 53, F32, 21) (dual of [53, 30, 22]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2168, 318, F2, 43) (dual of [318, 150, 44]-code), using
- linear OA(2167, 318, F2, 40) (dual of [318, 151, 41]-code), using Gilbert–Varšamov bound and bm = 2167 > Vbs−1(k−1) = 172 908879 428795 488259 464532 719681 893502 566648 417748 [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(2170, 321, F2, 43) (dual of [321, 151, 44]-code) | [i] | Adding a Parity Check Bit | |