Information on Result #721648
Linear OA(1671, 276, F16, 36) (dual of [276, 205, 37]-code), using construction XX applied to C1 = C([0,33]), C2 = C([8,35]), C3 = C1 + C2 = C([8,33]), and C∩ = C1 ∩ C2 = C([0,35]) based on
- linear OA(1660, 255, F16, 34) (dual of [255, 195, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(1652, 255, F16, 28) (dual of [255, 203, 29]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,35}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(1663, 255, F16, 36) (dual of [255, 192, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(1649, 255, F16, 26) (dual of [255, 206, 27]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,33}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(167, 17, F16, 7) (dual of [17, 10, 8]-code or 17-arc in PG(6,16)), using
- extended Reed–Solomon code RSe(10,16) [i]
- the expurgated narrow-sense BCH-code C(I) with length 17 | 162−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 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(1671, 138, F16, 2, 36) (dual of [(138, 2), 205, 37]-NRT-code) | [i] | OOA Folding | |