Information on Result #718085
Linear OA(982, 118, F9, 45) (dual of [118, 36, 46]-code), using construction XX applied to C1 = C([69,29]), C2 = C([1,33]), C3 = C1 + C2 = C([1,29]), and C∩ = C1 ∩ C2 = C([69,33]) based on
- linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−11,−10,…,29}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(951, 80, F9, 33) (dual of [80, 29, 34]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(965, 80, F9, 45) (dual of [80, 15, 46]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−11,−10,…,33}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(944, 80, F9, 29) (dual of [80, 36, 30]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(914, 28, F9, 11) (dual of [28, 14, 12]-code), using
- extended algebraic-geometric code AGe(F,16P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- extended algebraic-geometric code AGe(F,16P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- linear OA(93, 10, F9, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,9) or 10-cap in PG(2,9)), using
- extended Reed–Solomon code RSe(7,9) [i]
- oval in PG(2, 9) [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(983, 119, F9, 45) (dual of [119, 36, 46]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(981, 117, F9, 44) (dual of [117, 36, 45]-code) | [i] | Truncation | |
| 3 | Linear OOA(982, 59, F9, 2, 45) (dual of [(59, 2), 36, 46]-NRT-code) | [i] | OOA Folding | |