Information on Result #678587

Linear OA(4257, 65601, F4, 41) (dual of [65601, 65344, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
  1. linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  3. 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]

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(4257, 65601, F4, 40) (dual of [65601, 65344, 41]-code) [i]Strength Reduction
2Linear OA(4258, 65602, F4, 41) (dual of [65602, 65344, 42]-code) [i]Code Embedding in Larger Space
3Linear OA(4259, 65603, F4, 41) (dual of [65603, 65344, 42]-code) [i]
4Linear OA(4260, 65604, F4, 41) (dual of [65604, 65344, 42]-code) [i]
5Linear OA(4256, 65600, F4, 40) (dual of [65600, 65344, 41]-code) [i]Truncation
6Linear OOA(4257, 45919, F4, 2, 41) (dual of [(45919, 2), 91581, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Linear OOA(4257, 45919, F4, 3, 41) (dual of [(45919, 3), 137500, 42]-NRT-code) [i]
8Digital (216, 257, 45919)-net over F4 [i]
9Linear OA(4260, 65605, F4, 41) (dual of [65605, 65345, 42]-code) [i]Construction X with VarÅ¡amov Bound
10Linear OOA(4257, 32800, F4, 2, 41) (dual of [(32800, 2), 65343, 42]-NRT-code) [i]OOA Folding
11Linear OOA(4257, 21867, F4, 3, 41) (dual of [(21867, 3), 65344, 42]-NRT-code) [i]
12Linear OOA(4257, 3280, F4, 41, 41) (dual of [(3280, 41), 134223, 42]-NRT-code) [i]OOA Folding and Stacking with Additional Row