Information on Result #1301085

Linear OA(4245, 1048641, F4, 31) (dual of [1048641, 1048396, 32]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4241, 1048636, F4, 31) (dual of [1048636, 1048395, 32]-code), using
    • construction X applied to Ce(30) ⊂ Ce(24) [i] based on
      1. linear OA(4231, 1048576, F4, 31) (dual of [1048576, 1048345, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
      2. linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
  2. linear OA(4241, 1048637, F4, 27) (dual of [1048637, 1048396, 28]-code), using Gilbert–VarÅ¡amov bound and bm = 4241 > Vbs−1(k−1) = 21659 400181 827049 931943 523536 169065 835775 610026 770728 912707 325106 036782 022741 389284 354628 751635 649636 952932 252629 334673 049276 520378 408405 598569 [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(4245, 349547, F4, 3, 31) (dual of [(349547, 3), 1048396, 32]-NRT-code) [i]OOA Folding