Information on Result #684236

Linear OA(5110, 137, F5, 67) (dual of [137, 27, 68]-code), using construction XX applied to Ce(67) ⊂ Ce(62) ⊂ Ce(61) based on
  1. linear OA(5105, 125, F5, 68) (dual of [125, 20, 69]-code), using an extension Ce(67) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
  2. linear OA(599, 125, F5, 63) (dual of [125, 26, 64]-code), using an extension Ce(62) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
  3. linear OA(598, 125, F5, 62) (dual of [125, 27, 63]-code), using an extension Ce(61) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
  4. linear OA(54, 11, F5, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,5)), using
  5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), 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(5110, 137, F5, 66) (dual of [137, 27, 67]-code) [i]Strength Reduction
2Linear OA(5110, 137, F5, 65) (dual of [137, 27, 66]-code) [i]
3Linear OA(5110, 137, F5, 64) (dual of [137, 27, 65]-code) [i]
4Linear OA(5110, 137, F5, 63) (dual of [137, 27, 64]-code) [i]
5Linear OA(5113, 140, F5, 67) (dual of [140, 27, 68]-code) [i]Code Embedding in Larger Space
6Linear OA(5115, 143, F5, 67) (dual of [143, 28, 68]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(5116, 145, F5, 67) (dual of [145, 29, 68]-code) [i]
8Linear OOA(5110, 68, F5, 2, 67) (dual of [(68, 2), 26, 68]-NRT-code) [i]OOA Folding