Information on Result #942122
Linear OOA(9111, 57, F9, 2, 104) (dual of [(57, 2), 3, 105]-NRT-code), using juxtaposition based on
- linear OOA(953, 28, F9, 2, 51) (dual of [(28, 2), 3, 52]-NRT-code), using
- standard lengthening with (d0,…,d1) = (50,51) [i] based on linear OOA(951, 27, F9, 2, 49) (dual of [(27, 2), 3, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,4P) with known gap numbers [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using the Hermitian function field over F9 [i]
- linear OOA(955, 29, F9, 2, 52) (dual of [(29, 2), 3, 53]-NRT-code), using
- construction X applied to AG(2;F,0P) ⊂ AG(2;F,4P) [i] based on
- linear OOA(953, 27, F9, 2, 53) (dual of [(27, 2), 1, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,0P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28 (see above)
- linear OOA(951, 27, F9, 2, 49) (dual of [(27, 2), 3, 50]-NRT-code) (see above)
- linear OOA(92, 2, F9, 2, 2) (dual of [(2, 2), 2, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(92, 9, F9, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
- Reed–Solomon NRT-code RS(2;16,9) [i]
- discarding factors / shortening the dual code based on linear OOA(92, 9, F9, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
- construction X applied to AG(2;F,0P) ⊂ AG(2;F,4P) [i] based on
Mode: Constructive and 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 OOA(9111, 57, F9, 2, 103) (dual of [(57, 2), 3, 104]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(9111, 57, F9, 2, 102) (dual of [(57, 2), 3, 103]-NRT-code) | [i] | ||
| 3 | Linear OOA(9111, 57, F9, 2, 101) (dual of [(57, 2), 3, 102]-NRT-code) | [i] | ||
| 4 | Linear OOA(9108, 55, F9, 2, 101) (dual of [(55, 2), 2, 102]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(9107, 55, F9, 2, 100) (dual of [(55, 2), 3, 101]-NRT-code) | [i] | ||
| 6 | Linear OOA(9104, 53, F9, 2, 97) (dual of [(53, 2), 2, 98]-NRT-code) | [i] | ||
| 7 | Linear OOA(9103, 53, F9, 2, 96) (dual of [(53, 2), 3, 97]-NRT-code) | [i] | ||
| 8 | Linear OOA(9102, 52, F9, 2, 95) (dual of [(52, 2), 2, 96]-NRT-code) | [i] | ||
| 9 | Linear OOA(9100, 51, F9, 2, 93) (dual of [(51, 2), 2, 94]-NRT-code) | [i] | ||
| 10 | Linear OOA(999, 51, F9, 2, 92) (dual of [(51, 2), 3, 93]-NRT-code) | [i] | ||
| 11 | Linear OOA(995, 49, F9, 2, 88) (dual of [(49, 2), 3, 89]-NRT-code) | [i] | ||
| 12 | Linear OOA(992, 47, F9, 2, 85) (dual of [(47, 2), 2, 86]-NRT-code) | [i] | ||
| 13 | Linear OOA(991, 47, F9, 2, 84) (dual of [(47, 2), 3, 85]-NRT-code) | [i] | ||
| 14 | Linear OOA(990, 46, F9, 2, 83) (dual of [(46, 2), 2, 84]-NRT-code) | [i] | ||
| 15 | Linear OOA(986, 44, F9, 2, 79) (dual of [(44, 2), 2, 80]-NRT-code) | [i] | ||