Information on Result #1297605
Linear OA(2235, 348, F2, 66) (dual of [348, 113, 67]-code), using construction X with Varšamov bound based on
- linear OA(2232, 344, F2, 66) (dual of [344, 112, 67]-code), using
- 1 times truncation [i] based on linear OA(2233, 345, F2, 67) (dual of [345, 112, 68]-code), using
- concatenation of two codes [i] based on
- linear OA(1641, 69, F16, 33) (dual of [69, 28, 34]-code), using
- construction X applied to AG(F,30P) ⊂ AG(F,33P) [i] based on
- linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1636, 64, F16, 30) (dual of [64, 28, 31]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,30P) ⊂ AG(F,33P) [i] based on
- 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(1641, 69, F16, 33) (dual of [69, 28, 34]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2233, 345, F2, 67) (dual of [345, 112, 68]-code), using
- linear OA(2232, 345, F2, 63) (dual of [345, 113, 64]-code), using Gilbert–Varšamov bound and bm = 2232 > Vbs−1(k−1) = 2145 696774 106958 194329 448641 761380 441693 780475 355879 355922 986322 823208 [i]
- linear OA(22, 3, F2, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,2)), using
- dual of repetition code with length 3 [i]
- Hamming code H(2,2) [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(2236, 349, F2, 67) (dual of [349, 113, 68]-code) | [i] | Adding a Parity Check Bit | |