Information on Result #737140

Linear OA(4212, 4194375, F4, 24) (dual of [4194375, 4194163, 25]-code), using construction X applied to C([0,12]) ⊂ C([0,8]) based on
  1. linear OA(4199, 4194305, F4, 25) (dual of [4194305, 4194106, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  3. linear OA(413, 70, F4, 6) (dual of [70, 57, 7]-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(4213, 4194376, F4, 24) (dual of [4194376, 4194163, 25]-code) [i]Code Embedding in Larger Space
2Linear OA(4214, 4194377, F4, 24) (dual of [4194377, 4194163, 25]-code) [i]
3Linear OOA(4212, 2097187, F4, 2, 24) (dual of [(2097187, 2), 4194162, 25]-NRT-code) [i]OOA Folding
4Linear OOA(4212, 1398125, F4, 3, 24) (dual of [(1398125, 3), 4194163, 25]-NRT-code) [i]
5Linear OOA(4212, 349531, F4, 24, 24) (dual of [(349531, 24), 8388532, 25]-NRT-code) [i]OA Folding and Stacking