Information on Result #718024
Linear OA(976, 112, F9, 43) (dual of [112, 36, 44]-code), using construction XX applied to C1 = C([69,29]), C2 = C([1,31]), C3 = C1 + C2 = C([1,29]), and C∩ = C1 ∩ C2 = C([69,31]) 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(947, 80, F9, 31) (dual of [80, 33, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(961, 80, F9, 43) (dual of [80, 19, 44]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−11,−10,…,31}, and designed minimum distance d ≥ |I|+1 = 44 [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(91, 4, F9, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
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(977, 113, F9, 43) (dual of [113, 36, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(975, 111, F9, 42) (dual of [111, 36, 43]-code) | [i] | Truncation | |
| 3 | Linear OOA(976, 56, F9, 2, 43) (dual of [(56, 2), 36, 44]-NRT-code) | [i] | OOA Folding | |