Information on Result #1361884
Linear OOA(394, 88588, F3, 2, 12) (dual of [(88588, 2), 177082, 13]-NRT-code), using OOA 2-folding based on linear OA(394, 177176, F3, 12) (dual of [177176, 177082, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(394, 177177, F3, 12) (dual of [177177, 177083, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(390, 177171, F3, 12) (dual of [177171, 177081, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 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 Ce(12) ⊂ Ce(9) [i] based on
- linear OA(390, 177173, F3, 9) (dual of [177173, 177083, 10]-code), using Gilbert–Varšamov bound and bm = 390 > Vbs−1(k−1) = 6163 413608 145158 977671 819957 801215 511441 [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- linear OA(390, 177171, F3, 12) (dual of [177171, 177081, 13]-code), using
- construction X with Varšamov bound [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(394, 88588, F3, 3, 12) (dual of [(88588, 3), 265670, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(394, 88588, F3, 4, 12) (dual of [(88588, 4), 354258, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(394, 88588, F3, 5, 12) (dual of [(88588, 5), 442846, 13]-NRT-code) | [i] | ||
| 4 | Digital (82, 94, 88588)-net over F3 | [i] | ||