Information on Result #1299796

Linear OA(449, 262168, F4, 7) (dual of [262168, 262119, 8]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(447, 262164, F4, 7) (dual of [262164, 262117, 8]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. 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]
      3. linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
      4. linear OA(41, 20, F4, 1) (dual of [20, 19, 2]-code), using
  2. linear OA(447, 262166, F4, 6) (dual of [262166, 262119, 7]-code), using Gilbert–VarÅ¡amov bound and bm = 447 > Vbs−1(k−1) = 2507 753119 132685 823072 496960 [i]
  3. linear OA(40, 2, F4, 0) (dual of [2, 2, 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(449, 262168, F4, 2, 7) (dual of [(262168, 2), 524287, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(449, 262168, F4, 3, 7) (dual of [(262168, 3), 786455, 8]-NRT-code) [i]
3Digital (42, 49, 262168)-net over F4 [i]
4Linear OOA(449, 131084, F4, 2, 7) (dual of [(131084, 2), 262119, 8]-NRT-code) [i]OOA Folding