Information on Result #692525
Linear OA(16118, 262, F16, 71) (dual of [262, 144, 72]-code), using construction X applied to C([0,35]) ⊂ C([0,34]) based on
- linear OA(16117, 257, F16, 71) (dual of [257, 140, 72]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,35], and minimum distance d ≥ |{−35,−34,…,35}|+1 = 72 (BCH-bound) [i]
- linear OA(16113, 257, F16, 69) (dual of [257, 144, 70]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,34], and minimum distance d ≥ |{−34,−33,…,34}|+1 = 70 (BCH-bound) [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, s, F16, 1) (dual of [s, s−1, 2]-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 OA(16118, 262, F16, 70) (dual of [262, 144, 71]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16119, 263, F16, 71) (dual of [263, 144, 72]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(16120, 264, F16, 71) (dual of [264, 144, 72]-code) | [i] | ||
| 4 | Linear OA(16117, 261, F16, 70) (dual of [261, 144, 71]-code) | [i] | Truncation | |
| 5 | Linear OA(16115, 259, F16, 68) (dual of [259, 144, 69]-code) | [i] | ||
| 6 | Linear OA(16114, 258, F16, 67) (dual of [258, 144, 68]-code) | [i] | ||
| 7 | Linear OA(16111, 255, F16, 64) (dual of [255, 144, 65]-code) | [i] | ||
| 8 | Linear OA(16122, 268, F16, 71) (dual of [268, 146, 72]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(16123, 273, F16, 71) (dual of [273, 150, 72]-code) | [i] | ||
| 10 | Linear OA(16122, 267, F16, 71) (dual of [267, 145, 72]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(16118, 131, F16, 2, 71) (dual of [(131, 2), 144, 72]-NRT-code) | [i] | OOA Folding | |