Information on Result #722437
Linear OA(16123, 259, F16, 74) (dual of [259, 136, 75]-code), using construction XX applied to C1 = C([254,71]), C2 = C([0,72]), C3 = C1 + C2 = C([0,71]), and C∩ = C1 ∩ C2 = C([254,72]) based on
- linear OA(16121, 255, F16, 73) (dual of [255, 134, 74]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,71}, and designed minimum distance d ≥ |I|+1 = 74 [i]
- linear OA(16121, 255, F16, 73) (dual of [255, 134, 74]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,72], and designed minimum distance d ≥ |I|+1 = 74 [i]
- linear OA(16123, 255, F16, 74) (dual of [255, 132, 75]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,72}, and designed minimum distance d ≥ |I|+1 = 75 [i]
- linear OA(16119, 255, F16, 72) (dual of [255, 136, 73]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,71], and designed minimum distance d ≥ |I|+1 = 73 [i]
- 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
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code) (see above)
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 OA(16127, 271, F16, 74) (dual of [271, 144, 75]-code) | [i] | Varšamov–Edel Lengthening | |