Information on Result #1300839

Linear OA(4215, 1048641, F4, 27) (dual of [1048641, 1048426, 28]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-code), using
    • construction X applied to Ce(26) ⊂ Ce(20) [i] based on
      1. linear OA(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      2. linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
  2. linear OA(4211, 1048637, F4, 23) (dual of [1048637, 1048426, 24]-code), using Gilbert–VarÅ¡amov bound and bm = 4211 > Vbs−1(k−1) = 79 351139 376604 688502 492788 501714 450492 345168 814390 133024 777657 808608 948156 463540 117625 556295 703377 839108 810201 932577 783054 [i]
  3. linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), 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(4215, 349547, F4, 3, 27) (dual of [(349547, 3), 1048426, 28]-NRT-code) [i]OOA Folding