Information on Result #674309

Linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(3162, 4783018, F3, 17) (dual of [4783018, 4782856, 18]-code) [i]Code Embedding in Larger Space
2Linear OA(3163, 4783019, F3, 17) (dual of [4783019, 4782856, 18]-code) [i]
3Linear OA(3164, 4783020, F3, 17) (dual of [4783020, 4782856, 18]-code) [i]
4Linear OA(3165, 4783021, F3, 17) (dual of [4783021, 4782856, 18]-code) [i]
5Linear OA(3165, 4783022, F3, 17) (dual of [4783022, 4782857, 18]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(3161, 2391508, F3, 2, 17) (dual of [(2391508, 2), 4782855, 18]-NRT-code) [i]OOA Folding
7Linear OOA(3161, 1594339, F3, 3, 17) (dual of [(1594339, 3), 4782856, 18]-NRT-code) [i]
8Linear OOA(3161, 1195754, F3, 4, 17) (dual of [(1195754, 4), 4782855, 18]-NRT-code) [i]
9Linear OOA(3161, 956603, F3, 5, 17) (dual of [(956603, 5), 4782854, 18]-NRT-code) [i]
10Linear OOA(3161, 597877, F3, 17, 17) (dual of [(597877, 17), 10163748, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row