Information on Result #737264

Linear OA(4209, 16452, F4, 36) (dual of [16452, 16243, 37]-code), using construction X applied to Ce(36) ⊂ Ce(26) based on
  1. linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(419, 68, F4, 8) (dual of [68, 49, 9]-code), using
    • discarding factors / shortening the dual code based on linear OA(419, 69, F4, 8) (dual of [69, 50, 9]-code), using
      • construction XX applied to C1 = C({0,1,2,3,5,47}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,47}) [i] based on
        1. linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
        2. linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
        3. linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,47}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
        4. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
        5. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
        6. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)

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 OOA(4209, 8226, F4, 2, 36) (dual of [(8226, 2), 16243, 37]-NRT-code) [i]OOA Folding
2Linear OOA(4209, 5484, F4, 3, 36) (dual of [(5484, 3), 16243, 37]-NRT-code) [i]