Information on Result #731577
Linear OA(1660, 131084, F16, 15) (dual of [131084, 131024, 16]-code), using trace code based on linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 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(1661, 131085, F16, 15) (dual of [131085, 131024, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1660, 110190, F16, 2, 15) (dual of [(110190, 2), 220320, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (45, 60, 110190)-net over F16 | [i] | ||
| 4 | Linear OA(1661, 131086, F16, 15) (dual of [131086, 131025, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(1663, 131090, F16, 15) (dual of [131090, 131027, 16]-code) | [i] | ||
| 6 | Linear OOA(1660, 65542, F16, 2, 15) (dual of [(65542, 2), 131024, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1660, 18726, F16, 15, 15) (dual of [(18726, 15), 280830, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |