Information on Result #1299707

Linear OA(430, 262157, F4, 5) (dual of [262157, 262127, 6]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(429, 262155, F4, 5) (dual of [262155, 262126, 6]-code), using
    • construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
      1. linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      2. linear OA(419, 262144, F4, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
      3. linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
      4. linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
  2. linear OA(429, 262156, F4, 4) (dual of [262156, 262127, 5]-code), using Gilbert–VarÅ¡amov bound and bm = 429 > Vbs−1(k−1) = 81074 380037 952376 [i]
  3. linear OA(40, 1, F4, 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 OOA(430, 262157, F4, 2, 5) (dual of [(262157, 2), 524284, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(430, 262157, F4, 3, 5) (dual of [(262157, 3), 786441, 6]-NRT-code) [i]
3Digital (25, 30, 262157)-net over F4 [i]