Information on Result #1602521
Linear OOA(396, 9855, F3, 4, 15) (dual of [(9855, 4), 39324, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(396, 9855, F3, 2, 15) (dual of [(9855, 2), 19614, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(396, 19710, F3, 15) (dual of [19710, 19614, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(391, 19684, F3, 15) (dual of [19684, 19593, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 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
- linear OA(392, 19706, F3, 12) (dual of [19706, 19614, 13]-code), using Gilbert–Varšamov bound and bm = 392 > Vbs−1(k−1) = 8 900695 728292 029200 450900 974131 289283 431203 [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(392, 19704, F3, 15) (dual of [19704, 19612, 16]-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(396, 4927, F3, 20, 15) (dual of [(4927, 20), 98444, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |