Information on Result #678024

Linear OA(4198, 4194368, F4, 23) (dual of [4194368, 4194170, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
  1. linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
    • an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]

Mode: Constructive and 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 OA(4202, 4194374, F4, 23) (dual of [4194374, 4194172, 24]-code) [i]Construction X with VarÅ¡amov Bound
2Linear OA(4203, 4194376, F4, 23) (dual of [4194376, 4194173, 24]-code) [i]
3Linear OOA(4198, 2097184, F4, 2, 23) (dual of [(2097184, 2), 4194170, 24]-NRT-code) [i]OOA Folding
4Linear OOA(4198, 1398122, F4, 3, 23) (dual of [(1398122, 3), 4194168, 24]-NRT-code) [i]
5Linear OOA(4198, 381306, F4, 23, 23) (dual of [(381306, 23), 8769840, 24]-NRT-code) [i]OOA Folding and Stacking with Additional Row