Information on Result #962434
Linear OOA(4209, 1398119, F4, 3, 25) (dual of [(1398119, 3), 4194148, 26]-NRT-code), using OOA 3-folding based on linear OA(4209, 4194357, F4, 25) (dual of [4194357, 4194148, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4209, 4194359, F4, 25) (dual of [4194359, 4194150, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4199, 4194305, F4, 25) (dual of [4194305, 4194106, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4155, 4194305, F4, 19) (dual of [4194305, 4194150, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 54, F4, 5) (dual of [54, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
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 | Digital (184, 209, 1398119)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |