Information on Result #678431

Linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), 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(4114, 262176, F4, 16) (dual of [262176, 262062, 17]-code) [i]Strength Reduction
2Linear OA(4115, 262177, F4, 17) (dual of [262177, 262062, 18]-code) [i]Code Embedding in Larger Space
3Linear OA(4116, 262178, F4, 17) (dual of [262178, 262062, 18]-code) [i]
4Linear OA(4117, 262179, F4, 17) (dual of [262179, 262062, 18]-code) [i]
5Linear OA(4113, 262175, F4, 16) (dual of [262175, 262062, 17]-code) [i]Truncation
6Linear OA(4117, 262180, F4, 17) (dual of [262180, 262063, 18]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(4118, 262182, F4, 17) (dual of [262182, 262064, 18]-code) [i]
8Linear OOA(4114, 131088, F4, 2, 17) (dual of [(131088, 2), 262062, 18]-NRT-code) [i]OOA Folding
9Linear OOA(4114, 87392, F4, 3, 17) (dual of [(87392, 3), 262062, 18]-NRT-code) [i]
10Linear OOA(4114, 32771, F4, 17, 17) (dual of [(32771, 17), 556993, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row