Information on Result #718442
Linear OA(9111, 127, F9, 74) (dual of [127, 16, 75]-code), using construction XX applied to C1 = C([11,79]), C2 = C([1,59]), C3 = C1 + C2 = C([11,59]), and C∩ = C1 ∩ C2 = C([1,79]) based on
- linear OA(976, 80, F9, 69) (dual of [80, 4, 70]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,79}, and designed minimum distance d ≥ |I|+1 = 70 [i]
- linear OA(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,59], and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(979, 80, F9, 79) (dual of [80, 1, 80]-code or 80-arc in PG(78,9)), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(964, 80, F9, 49) (dual of [80, 16, 50]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,59}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(918, 30, F9, 14) (dual of [30, 12, 15]-code), using
- extended algebraic-geometric code AGe(F,15P) [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- linear OA(910, 17, F9, 9) (dual of [17, 7, 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(9111, 127, F9, 73) (dual of [127, 16, 74]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(9111, 127, F9, 72) (dual of [127, 16, 73]-code) | [i] | ||
| 3 | Linear OA(9110, 126, F9, 73) (dual of [126, 16, 74]-code) | [i] | Truncation | |
| 4 | Linear OA(9107, 123, F9, 70) (dual of [123, 16, 71]-code) | [i] | ||