Information on Result #718302
Linear OA(9100, 125, F9, 61) (dual of [125, 25, 62]-code), using construction XX applied to C1 = C([11,61]), C2 = C([1,49]), C3 = C1 + C2 = C([11,49]), and C∩ = C1 ∩ C2 = C([1,61]) based on
- linear OA(967, 80, F9, 51) (dual of [80, 13, 52]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,61}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(964, 80, F9, 49) (dual of [80, 16, 50]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(974, 80, F9, 61) (dual of [80, 6, 62]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,49}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(914, 26, F9, 11) (dual of [26, 12, 12]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(914, 28, F9, 11) (dual of [28, 14, 12]-code), using
- linear OA(910, 19, F9, 9) (dual of [19, 9, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-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(9100, 125, F9, 60) (dual of [125, 25, 61]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(9101, 126, F9, 61) (dual of [126, 25, 62]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(9102, 127, F9, 61) (dual of [127, 25, 62]-code) | [i] | ||
| 4 | Linear OA(999, 124, F9, 60) (dual of [124, 25, 61]-code) | [i] | Truncation | |
| 5 | Linear OA(998, 123, F9, 59) (dual of [123, 25, 60]-code) | [i] | ||
| 6 | Linear OA(996, 121, F9, 57) (dual of [121, 25, 58]-code) | [i] | ||
| 7 | Linear OA(995, 120, F9, 56) (dual of [120, 25, 57]-code) | [i] | ||