Information on Result #674753

Linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) based on
  1. linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
    • the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]

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(3119, 177188, F3, 15) (dual of [177188, 177069, 16]-code) [i]Strength Reduction
2Linear OA(3120, 177189, F3, 16) (dual of [177189, 177069, 17]-code) [i]Code Embedding in Larger Space
3Linear OA(3118, 177187, F3, 15) (dual of [177187, 177069, 16]-code) [i]Truncation
4Linear OOA(3119, 88594, F3, 2, 16) (dual of [(88594, 2), 177069, 17]-NRT-code) [i]OOA Folding
5Linear OOA(3119, 59062, F3, 3, 16) (dual of [(59062, 3), 177067, 17]-NRT-code) [i]
6Linear OOA(3119, 44297, F3, 4, 16) (dual of [(44297, 4), 177069, 17]-NRT-code) [i]
7Linear OOA(3119, 35437, F3, 5, 16) (dual of [(35437, 5), 177066, 17]-NRT-code) [i]
8Linear OOA(3119, 22148, F3, 16, 16) (dual of [(22148, 16), 354249, 17]-NRT-code) [i]OA Folding and Stacking