Information on Result #686962

Linear OA(8172, 32833, F8, 36) (dual of [32833, 32661, 37]-code), using construction X applied to Ce(35) ⊂ Ce(24) based on
  1. linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
  2. linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(816, 65, F8, 10) (dual of [65, 49, 11]-code), using
    • the BCH-code C(I) with length 65 | 84−1, defining interval I = {1,8,15,…,64}, and designed minimum distance d ≥ |I|+1 = 11 [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(8173, 32834, F8, 36) (dual of [32834, 32661, 37]-code) [i]Code Embedding in Larger Space
2Linear OOA(8172, 16416, F8, 2, 36) (dual of [(16416, 2), 32660, 37]-NRT-code) [i]OOA Folding
3Linear OOA(8172, 10944, F8, 3, 36) (dual of [(10944, 3), 32660, 37]-NRT-code) [i]
4Linear OOA(8172, 1824, F8, 36, 36) (dual of [(1824, 36), 65492, 37]-NRT-code) [i]OA Folding and Stacking