Information on Result #721921
Linear OA(16103, 282, F16, 54) (dual of [282, 179, 55]-code), using construction XX applied to C1 = C([254,50]), C2 = C([9,52]), C3 = C1 + C2 = C([9,50]), and C∩ = C1 ∩ C2 = C([254,52]) 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(1679, 255, F16, 44) (dual of [255, 176, 45]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {9,10,…,52}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(1692, 255, F16, 54) (dual of [255, 163, 55]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,52}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(1676, 255, F16, 42) (dual of [255, 179, 43]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {9,10,…,50}, and designed minimum distance d ≥ |I|+1 = 43 [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(161, 4, F16, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16103, 141, F16, 2, 54) (dual of [(141, 2), 179, 55]-NRT-code) | [i] | OOA Folding | |