Information on Result #722155
Linear OA(16120, 292, F16, 61) (dual of [292, 172, 62]-code), using construction XX applied to C1 = C([251,51]), C2 = C([6,56]), C3 = C1 + C2 = C([6,51]), and C∩ = C1 ∩ C2 = C([251,56]) based on
- linear OA(1696, 255, F16, 56) (dual of [255, 159, 57]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−4,−3,…,51}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(1693, 255, F16, 51) (dual of [255, 162, 52]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,56}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(16106, 255, F16, 61) (dual of [255, 149, 62]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−4,−3,…,56}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(1683, 255, F16, 46) (dual of [255, 172, 47]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,51}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(1610, 23, F16, 9) (dual of [23, 13, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(1610, 24, F16, 9) (dual of [24, 14, 10]-code), using
- extended algebraic-geometric code AGe(F,14P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(1610, 24, F16, 9) (dual of [24, 14, 10]-code), using
- linear OA(164, 14, F16, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16120, 146, F16, 2, 61) (dual of [(146, 2), 172, 62]-NRT-code) | [i] | OOA Folding | |