Information on Result #718484
Linear OA(9114, 128, F9, 78) (dual of [128, 14, 79]-code), using construction XX applied to C1 = C([61,49]), C2 = C([0,59]), C3 = C1 + C2 = C([0,49]), and C∩ = C1 ∩ C2 = C([61,59]) 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 = {−19,−18,…,49}, and designed minimum distance d ≥ |I|+1 = 70 [i]
- linear OA(972, 80, F9, 60) (dual of [80, 8, 61]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,59], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(979, 80, F9, 79) (dual of [80, 1, 80]-code or 80-arc in PG(78,9)), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−19,−18,…,59}, and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(965, 80, F9, 50) (dual of [80, 15, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(922, 32, F9, 17) (dual of [32, 10, 18]-code), using
- extended algebraic-geometric code AGe(F,14P) [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- algebraic-geometric code AG(F,7P) with degP = 2 [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using a function field by Sémirat [i]
- linear OA(910, 16, F9, 9) (dual of [16, 6, 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 OOA(9114, 64, F9, 2, 78) (dual of [(64, 2), 14, 79]-NRT-code) | [i] | OOA Folding | |