Information on Result #678723

Linear OA(4256, 65575, F4, 42) (dual of [65575, 65319, 43]-code), using construction X applied to Ce(41) ⊂ Ce(36) based on
  1. linear OA(4249, 65536, F4, 42) (dual of [65536, 65287, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
  2. linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-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(4257, 65576, F4, 42) (dual of [65576, 65319, 43]-code) [i]Code Embedding in Larger Space
2Linear OA(4258, 65577, F4, 42) (dual of [65577, 65319, 43]-code) [i]
3Linear OA(4259, 65578, F4, 42) (dual of [65578, 65319, 43]-code) [i]
4Linear OA(4260, 65579, F4, 42) (dual of [65579, 65319, 43]-code) [i]
5Linear OOA(4256, 36176, F4, 2, 42) (dual of [(36176, 2), 72096, 43]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4256, 36176, F4, 3, 42) (dual of [(36176, 3), 108272, 43]-NRT-code) [i]
7Digital (214, 256, 36176)-net over F4 [i]
8Linear OA(4260, 65580, F4, 42) (dual of [65580, 65320, 43]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(4256, 32787, F4, 2, 42) (dual of [(32787, 2), 65318, 43]-NRT-code) [i]OOA Folding
10Linear OOA(4256, 21858, F4, 3, 42) (dual of [(21858, 3), 65318, 43]-NRT-code) [i]