Information on Result #721866
Linear OA(16102, 284, F16, 53) (dual of [284, 182, 54]-code), using construction XX applied to C1 = C([0,51]), C2 = C([11,52]), C3 = C1 + C2 = C([11,51]), and C∩ = C1 ∩ C2 = C([0,52]) based on
- linear OA(1688, 255, F16, 52) (dual of [255, 167, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(1675, 255, F16, 42) (dual of [255, 180, 43]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {11,12,…,52}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(1690, 255, F16, 53) (dual of [255, 165, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(1673, 255, F16, 41) (dual of [255, 182, 42]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {11,12,…,51}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(1612, 27, F16, 10) (dual of [27, 15, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1612, 33, F16, 10) (dual of [33, 21, 11]-code), using
- extended algebraic-geometric code AGe(F,22P) [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(1612, 33, F16, 10) (dual of [33, 21, 11]-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(16102, 142, F16, 2, 53) (dual of [(142, 2), 182, 54]-NRT-code) | [i] | OOA Folding | |