Information on Result #721897
Linear OA(16109, 292, F16, 55) (dual of [292, 183, 56]-code), using construction XX applied to C1 = C([254,50]), C2 = C([11,53]), C3 = C1 + C2 = C([11,50]), and C∩ = C1 ∩ C2 = C([254,53]) based on
- linear OA(1689, 255, F16, 52) (dual of [255, 166, 53]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,50}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(1677, 255, F16, 43) (dual of [255, 178, 44]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {11,12,…,53}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(1694, 255, F16, 55) (dual of [255, 161, 56]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,53}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(1672, 255, F16, 40) (dual of [255, 183, 41]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {11,12,…,50}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(1613, 30, F16, 11) (dual of [30, 17, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(1613, 33, F16, 11) (dual of [33, 20, 12]-code), using
- extended algebraic-geometric code AGe(F,21P) [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- discarding factors / shortening the dual code based on linear OA(1613, 33, F16, 11) (dual of [33, 20, 12]-code), using
- linear OA(162, 7, F16, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(16109, 146, F16, 2, 55) (dual of [(146, 2), 183, 56]-NRT-code) | [i] | OOA Folding | |