Information on Result #1521954
Linear OOA(3102, 265736, F3, 3, 12) (dual of [(265736, 3), 797106, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3102, 265736, F3, 2, 12) (dual of [(265736, 2), 531370, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3102, 531472, F3, 12) (dual of [531472, 531370, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3102, 531473, F3, 12) (dual of [531473, 531371, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(398, 531467, F3, 12) (dual of [531467, 531369, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 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(398, 531469, F3, 9) (dual of [531469, 531371, 10]-code), using Gilbert–Varšamov bound and bm = 398 > Vbs−1(k−1) = 40 412600 174106 948585 131762 490626 303838 690289 [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(398, 531467, F3, 12) (dual of [531467, 531369, 13]-code), using
- construction X with Varšamov bound [i] based on
- discarding factors / shortening the dual code based on linear OA(3102, 531473, F3, 12) (dual of [531473, 531371, 13]-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(3102, 132868, F3, 5, 12) (dual of [(132868, 5), 664238, 13]-NRT-code) | [i] | OOA Folding | |