Information on Result #692784
Linear OA(16122, 266, F16, 72) (dual of [266, 144, 73]-code), using construction X applied to Ce(71) ⊂ Ce(67) based on
- linear OA(16119, 256, F16, 72) (dual of [256, 137, 73]-code), using an extension Ce(71) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,71], and designed minimum distance d ≥ |I|+1 = 72 [i]
- linear OA(16112, 256, F16, 68) (dual of [256, 144, 69]-code), using an extension Ce(67) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(163, 10, F16, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,16) or 10-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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 OA(16122, 266, F16, 71) (dual of [266, 144, 72]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16125, 269, F16, 72) (dual of [269, 144, 73]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(16121, 265, F16, 71) (dual of [265, 144, 72]-code) | [i] | Truncation | |
| 4 | Linear OA(16124, 269, F16, 72) (dual of [269, 145, 73]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(16122, 133, F16, 2, 72) (dual of [(133, 2), 144, 73]-NRT-code) | [i] | OOA Folding | |