Information on Result #737332

Linear OA(4255, 4164, F4, 52) (dual of [4164, 3909, 53]-code), using construction X applied to Ce(52) ⊂ Ce(41) based on
  1. linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
  2. linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
  3. linear OA(420, 68, F4, 9) (dual of [68, 48, 10]-code), using
    • construction X applied to Ce(8) ⊂ Ce(6) [i] based on
      1. linear OA(419, 64, F4, 9) (dual of [64, 45, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using

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(4256, 4165, F4, 52) (dual of [4165, 3909, 53]-code) [i]Code Embedding in Larger Space
2Linear OOA(4255, 2082, F4, 2, 52) (dual of [(2082, 2), 3909, 53]-NRT-code) [i]OOA Folding
3Linear OOA(4255, 1388, F4, 3, 52) (dual of [(1388, 3), 3909, 53]-NRT-code) [i]