Information on Result #1361943
Linear OOA(3174, 29552, F3, 2, 24) (dual of [(29552, 2), 58930, 25]-NRT-code), using OOA 2-folding based on linear OA(3174, 59104, F3, 24) (dual of [59104, 58930, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3170, 59099, F3, 24) (dual of [59099, 58929, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(39, 49, F3, 4) (dual of [49, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3170, 59100, F3, 20) (dual of [59100, 58930, 21]-code), using Gilbert–Varšamov bound and bm = 3170 > Vbs−1(k−1) = 19 647663 364515 428307 323077 719525 878234 129146 170108 217591 012313 925788 230854 612155 [i]
- linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2, 3) [i]
- linear OA(3170, 59099, F3, 24) (dual of [59099, 58929, 25]-code), using
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(3174, 29552, F3, 3, 24) (dual of [(29552, 3), 88482, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3174, 29552, F3, 4, 24) (dual of [(29552, 4), 118034, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3174, 29552, F3, 5, 24) (dual of [(29552, 5), 147586, 25]-NRT-code) | [i] | ||
| 4 | Digital (150, 174, 29552)-net over F3 | [i] | ||