Information on Result #1301494

Linear OA(577, 142, F5, 36) (dual of [142, 65, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(576, 140, F5, 36) (dual of [140, 64, 37]-code), using
    • construction XX applied to Ce(36) ⊂ Ce(31) ⊂ Ce(30) [i] based on
      1. linear OA(571, 125, F5, 37) (dual of [125, 54, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
      2. linear OA(562, 125, F5, 32) (dual of [125, 63, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
      3. linear OA(561, 125, F5, 31) (dual of [125, 64, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
      4. linear OA(54, 14, F5, 3) (dual of [14, 10, 4]-code or 14-cap in PG(3,5)), using
      5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
  2. linear OA(576, 141, F5, 35) (dual of [141, 65, 36]-code), using Gilbert–VarÅ¡amov bound and bm = 576 > Vbs−1(k−1) = 127502 473082 845565 271512 326702 110954 119820 781605 218385 [i]
  3. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), 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 OA(578, 144, F5, 36) (dual of [144, 66, 37]-code) [i]Construction X with VarÅ¡amov Bound