Information on Result #2486056
Linear OOA(3136, 797178, F3, 2, 15) (dual of [(797178, 2), 1594220, 16]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(3132, 797176, F3, 2, 15) (dual of [(797176, 2), 1594220, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3132, 1594352, F3, 15) (dual of [1594352, 1594220, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3131, 1594324, F3, 15) (dual of [1594324, 1594193, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3105, 1594324, F3, 13) (dual of [1594324, 1594219, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [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(3136, 562570, F3, 3, 15) (dual of [(562570, 3), 1687574, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3136, 562570, F3, 4, 15) (dual of [(562570, 4), 2250144, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3136, 562570, F3, 5, 15) (dual of [(562570, 5), 2812714, 16]-NRT-code) | [i] | ||
| 4 | Digital (121, 136, 562570)-net over F3 | [i] | ||