Information on Result #1299737

Linear OA(436, 4194319, F4, 5) (dual of [4194319, 4194283, 6]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(435, 4194317, F4, 5) (dual of [4194317, 4194282, 6]-code), using
    • construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
      1. linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      2. linear OA(423, 4194304, F4, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
      3. linear OA(412, 13, F4, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
      4. linear OA(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
  2. linear OA(435, 4194318, F4, 4) (dual of [4194318, 4194283, 5]-code), using Gilbert–VarÅ¡amov bound and bm = 435 > Vbs−1(k−1) = 332 044322 434367 627536 [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(436, 4194319, F4, 2, 5) (dual of [(4194319, 2), 8388602, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(436, 4194319, F4, 3, 5) (dual of [(4194319, 3), 12582921, 6]-NRT-code) [i]
3Digital (31, 36, 4194319)-net over F4 [i]