Information on Result #1298785

Linear OA(3162, 1594356, F3, 18) (dual of [1594356, 1594194, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3158, 1594351, F3, 18) (dual of [1594351, 1594193, 19]-code), using
    • construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
      1. linear OA(3157, 1594323, F3, 19) (dual of [1594323, 1594166, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
      4. linear OA(31, 28, F3, 1) (dual of [28, 27, 2]-code), using
  2. linear OA(3158, 1594352, F3, 14) (dual of [1594352, 1594194, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 3158 > Vbs−1(k−1) = 565 823982 943625 959323 760589 566519 711256 987096 037859 333062 704173 505235 911403 [i]
  3. linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), 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:

ResultThis
result
only		Method
1Linear OOA(3162, 797178, F3, 2, 18) (dual of [(797178, 2), 1594194, 19]-NRT-code) [i]OOA Folding
2Linear OOA(3162, 531452, F3, 3, 18) (dual of [(531452, 3), 1594194, 19]-NRT-code) [i]
3Linear OOA(3162, 398589, F3, 4, 18) (dual of [(398589, 4), 1594194, 19]-NRT-code) [i]