Information on Result #678995

Linear OA(4185, 16443, F4, 33) (dual of [16443, 16258, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,12]) based on
  1. linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  2. linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  3. linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-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(4185, 16443, F4, 32) (dual of [16443, 16258, 33]-code) [i]Strength Reduction
2Linear OA(4186, 16444, F4, 33) (dual of [16444, 16258, 34]-code) [i]Code Embedding in Larger Space
3Linear OA(4187, 16445, F4, 33) (dual of [16445, 16258, 34]-code) [i]
4Linear OA(4184, 16442, F4, 32) (dual of [16442, 16258, 33]-code) [i]Truncation
5Linear OA(4187, 16446, F4, 33) (dual of [16446, 16259, 34]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(4185, 8221, F4, 2, 33) (dual of [(8221, 2), 16257, 34]-NRT-code) [i]OOA Folding
7Linear OOA(4185, 5481, F4, 3, 33) (dual of [(5481, 3), 16258, 34]-NRT-code) [i]