Information on Result #1011940

Linear OOA(4165, 2797571, F4, 3, 15) (dual of [(2797571, 3), 8392548, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(432, 1370, F4, 3, 7) (dual of [(1370, 3), 4078, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(432, 4110, F4, 7) (dual of [4110, 4078, 8]-code), using
      • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
        1. linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(419, 4096, F4, 5) (dual of [4096, 4077, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
        3. linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
        4. linear OA(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
  2. linear OOA(4133, 2796201, F4, 3, 15) (dual of [(2796201, 3), 8388470, 16]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(4133, large, F4, 15) (dual of [large, large−133, 16]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(4166, 2797571, F4, 3, 15) (dual of [(2797571, 3), 8392547, 16]-NRT-code) [i]OOA Duplication