Information on Result #722417
Linear OA(16120, 262, F16, 72) (dual of [262, 142, 73]-code), using construction XX applied to C1 = C([253,68]), C2 = C([0,69]), C3 = C1 + C2 = C([0,68]), and C∩ = C1 ∩ C2 = C([253,69]) based on
- linear OA(16117, 255, F16, 71) (dual of [255, 138, 72]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,68}, and designed minimum distance d ≥ |I|+1 = 72 [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(16119, 255, F16, 72) (dual of [255, 136, 73]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,69}, and designed minimum distance d ≥ |I|+1 = 73 [i]
- 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(161, 5, F16, 1) (dual of [5, 4, 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
- 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(16120, 131, F16, 2, 72) (dual of [(131, 2), 142, 73]-NRT-code) | [i] | OOA Folding | |