Information on Result #823516
Linear OOA(4157, 2097165, F4, 2, 19) (dual of [(2097165, 2), 4194173, 20]-NRT-code), using OOA 2-folding based on linear OA(4157, 4194330, F4, 19) (dual of [4194330, 4194173, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4156, 4194329, F4, 19) (dual of [4194329, 4194173, 20]-code), using
- construction X4 applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 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(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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 X4 applied to C([0,9]) ⊂ C([0,8]) [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 | Linear OOA(4159, 2097166, F4, 2, 19) (dual of [(2097166, 2), 4194173, 20]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4158, 2097165, F4, 2, 19) (dual of [(2097165, 2), 4194172, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4157, 1541240, F4, 3, 19) (dual of [(1541240, 3), 4623563, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (138, 157, 1541240)-net over F4 | [i] | ||