Information on Result #679127

Linear OA(4153, 16410, F4, 29) (dual of [16410, 16257, 30]-code), using construction X applied to Ce(28) ⊂ Ce(24) based on
  1. linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  2. linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), 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(4153, 16410, F4, 28) (dual of [16410, 16257, 29]-code) [i]Strength Reduction
2Linear OA(4154, 16411, F4, 29) (dual of [16411, 16257, 30]-code) [i]Code Embedding in Larger Space
3Linear OA(4152, 16409, F4, 28) (dual of [16409, 16257, 29]-code) [i]Truncation
4Linear OOA(4153, 8905, F4, 2, 29) (dual of [(8905, 2), 17657, 30]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4153, 8905, F4, 3, 29) (dual of [(8905, 3), 26562, 30]-NRT-code) [i]
6Digital (124, 153, 8905)-net over F4 [i]
7Linear OOA(4153, 8205, F4, 2, 29) (dual of [(8205, 2), 16257, 30]-NRT-code) [i]OOA Folding
8Linear OOA(4153, 5470, F4, 3, 29) (dual of [(5470, 3), 16257, 30]-NRT-code) [i]
9Linear OOA(4153, 1172, F4, 29, 29) (dual of [(1172, 29), 33835, 30]-NRT-code) [i]OOA Folding and Stacking with Additional Row