Information on Result #1546684
Linear OOA(4258, 32777, F4, 3, 43) (dual of [(32777, 3), 98073, 44]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4258, 32777, F4, 2, 43) (dual of [(32777, 2), 65296, 44]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4258, 65554, F4, 43) (dual of [65554, 65296, 44]-code), using
- construction X applied to C([0,21]) ⊂ C([0,20]) [i] based on
- linear OA(4257, 65537, F4, 43) (dual of [65537, 65280, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,21]) ⊂ C([0,20]) [i] based on
Mode: 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(4258, 4682, F4, 45, 43) (dual of [(4682, 45), 210432, 44]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |