Information on Result #735554

Linear OA(12876, 16776, F128, 27) (dual of [16776, 16700, 28]-code), using (u, u+v)-construction based on
  1. linear OA(12822, 386, F128, 13) (dual of [386, 364, 14]-code), using
    • construction X applied to Ce(12) ⊂ Ce(10) [i] based on
      1. linear OA(12821, 382, F128, 13) (dual of [382, 361, 14]-code), using an extension Ce(12) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(12818, 382, F128, 11) (dual of [382, 364, 12]-code), using an extension Ce(10) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(1281, 4, F128, 1) (dual of [4, 3, 2]-code), using
  2. linear OA(12854, 16390, F128, 27) (dual of [16390, 16336, 28]-code), using
    • construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
      1. linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
      2. linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      3. linear OA(1281, 5, F128, 1) (dual of [5, 4, 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 OOA(12876, 8388, F128, 2, 27) (dual of [(8388, 2), 16700, 28]-NRT-code) [i]OOA Folding
2Linear OOA(12876, 5592, F128, 3, 27) (dual of [(5592, 3), 16700, 28]-NRT-code) [i]