Information on Result #722341
Linear OA(16125, 278, F16, 70) (dual of [278, 153, 71]-code), using construction XX applied to C1 = C([0,68]), C2 = C([10,69]), C3 = C1 + C2 = C([10,68]), and C∩ = C1 ∩ C2 = C([0,69]) based on
- linear OA(16113, 255, F16, 69) (dual of [255, 142, 70]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,68], and designed minimum distance d ≥ |I|+1 = 70 [i]
- linear OA(16104, 255, F16, 60) (dual of [255, 151, 61]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {10,11,…,69}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(16115, 255, F16, 70) (dual of [255, 140, 71]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,69], and designed minimum distance d ≥ |I|+1 = 71 [i]
- linear OA(16102, 255, F16, 59) (dual of [255, 153, 60]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {10,11,…,68}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(1610, 21, F16, 9) (dual of [21, 11, 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(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(16125, 139, F16, 2, 70) (dual of [(139, 2), 153, 71]-NRT-code) | [i] | OOA Folding | |