Information on Result #627677

Linear OA(350, 56, F3, 35) (dual of [56, 6, 36]-code), using dual code (with bound on d by construction Y1) based on
  1. linear OA(36, 56, F3, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
  2. nonexistence of linear OA(35, 21, F3, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because

Mode: Constructive and 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(350, 56, F3, 34) (dual of [56, 6, 35]-code) [i]Strength Reduction
2Linear OA(350, 56, F3, 33) (dual of [56, 6, 34]-code) [i]
3Linear OA(350, 56, F3, 32) (dual of [56, 6, 33]-code) [i]
4Linear OA(350, 56, F3, 31) (dual of [56, 6, 32]-code) [i]
5Linear OA(351, 57, F3, 35) (dual of [57, 6, 36]-code) [i]Code Embedding in Larger Space
6Linear OA(352, 58, F3, 35) (dual of [58, 6, 36]-code) [i]
7Linear OA(353, 59, F3, 35) (dual of [59, 6, 36]-code) [i]
8Linear OA(354, 60, F3, 35) (dual of [60, 6, 36]-code) [i]
9Linear OA(349, 55, F3, 34) (dual of [55, 6, 35]-code) [i]Truncation
10Linear OA(348, 54, F3, 33) (dual of [54, 6, 34]-code) [i]
11Linear OA(347, 53, F3, 32) (dual of [53, 6, 33]-code) [i]
12Linear OA(346, 52, F3, 31) (dual of [52, 6, 32]-code) [i]
13Linear OA(345, 51, F3, 30) (dual of [51, 6, 31]-code) [i]
14Linear OA(360, 66, F3, 39) (dual of [66, 6, 40]-code) [i]Juxtaposition
15Linear OA(361, 67, F3, 40) (dual of [67, 6, 41]-code) [i]
16Linear OA(362, 68, F3, 41) (dual of [68, 6, 42]-code) [i]
17Linear OA(379, 85, F3, 51) (dual of [85, 6, 52]-code) [i]
18Linear OA(380, 86, F3, 52) (dual of [86, 6, 53]-code) [i]
19Linear OA(355, 60, F3, 36) (dual of [60, 5, 37]-code) [i]
20Linear OA(356, 61, F3, 37) (dual of [61, 5, 38]-code) [i]
21Linear OA(359, 64, F3, 39) (dual of [64, 5, 40]-code) [i]
22Linear OA(360, 65, F3, 40) (dual of [65, 5, 41]-code) [i]
23Linear OA(361, 66, F3, 41) (dual of [66, 5, 42]-code) [i]
24Linear OA(3131, 136, F3, 89) (dual of [136, 5, 90]-code) [i]
25Linear OA(315, 20, F3, 11) (dual of [20, 5, 12]-code) [i]Residual Code
26Linear OA(3159, 165, F3, 107) (dual of [165, 6, 108]-code) [i](u, u−v, u+v+w)-Construction
27Linear OA(3161, 168, F3, 107) (dual of [168, 7, 108]-code) [i]
28Linear OA(3210, 217, F3, 136) (dual of [217, 7, 137]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
29Linear OOA(350, 28, F3, 2, 35) (dual of [(28, 2), 6, 36]-NRT-code) [i]OOA Folding
30Linear OOA(350, 14, F3, 4, 35) (dual of [(14, 4), 6, 36]-NRT-code) [i]