Information on Result #678740

Linear OA(4120, 65575, F4, 19) (dual of [65575, 65455, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
  1. linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(481, 65536, F4, 14) (dual of [65536, 65455, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(4121, 65576, F4, 19) (dual of [65576, 65455, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(4122, 65577, F4, 19) (dual of [65577, 65455, 20]-code) [i]
3Linear OOA(4120, 39183, F4, 2, 19) (dual of [(39183, 2), 78246, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4120, 39183, F4, 3, 19) (dual of [(39183, 3), 117429, 20]-NRT-code) [i]
5Digital (101, 120, 39183)-net over F4 [i]
6Linear OA(4122, 65578, F4, 19) (dual of [65578, 65456, 20]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(4120, 32787, F4, 2, 19) (dual of [(32787, 2), 65454, 20]-NRT-code) [i]OOA Folding
8Linear OOA(4120, 21858, F4, 3, 19) (dual of [(21858, 3), 65454, 20]-NRT-code) [i]
9Linear OOA(4120, 7286, F4, 19, 19) (dual of [(7286, 19), 138314, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row