Information on Result #1361886
Linear OOA(3110, 797178, F3, 2, 12) (dual of [(797178, 2), 1594246, 13]-NRT-code), using OOA 2-folding based on linear OA(3110, 1594356, F3, 12) (dual of [1594356, 1594246, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, 1594357, F3, 12) (dual of [1594357, 1594247, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3106, 1594351, F3, 12) (dual of [1594351, 1594245, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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 Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3106, 1594353, F3, 9) (dual of [1594353, 1594247, 10]-code), using Gilbert–Varšamov bound and bm = 3106 > Vbs−1(k−1) = 265085 877710 653561 599327 960431 322500 144166 373569 [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(3106, 1594351, F3, 12) (dual of [1594351, 1594245, 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(3110, 797178, F3, 3, 12) (dual of [(797178, 3), 2391424, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3110, 797178, F3, 4, 12) (dual of [(797178, 4), 3188602, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3110, 797178, F3, 5, 12) (dual of [(797178, 5), 3985780, 13]-NRT-code) | [i] | ||
| 4 | Digital (98, 110, 797178)-net over F3 | [i] | ||