Information on Result #699238

Linear OA(8165, 531460, F81, 21) (dual of [531460, 531395, 22]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
  1. linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  3. linear OA(814, 19, F81, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,81)), 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 OOA(8165, 265884, F81, 2, 21) (dual of [(265884, 2), 531703, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8165, 265884, F81, 3, 21) (dual of [(265884, 3), 797587, 22]-NRT-code) [i]
3Linear OOA(8165, 265884, F81, 4, 21) (dual of [(265884, 4), 1063471, 22]-NRT-code) [i]
4Digital (44, 65, 265884)-net over F81 [i]
5Linear OOA(8165, 265730, F81, 2, 21) (dual of [(265730, 2), 531395, 22]-NRT-code) [i]OOA Folding
6Linear OOA(8165, 177153, F81, 3, 21) (dual of [(177153, 3), 531394, 22]-NRT-code) [i]
7Linear OOA(8165, 132865, F81, 4, 21) (dual of [(132865, 4), 531395, 22]-NRT-code) [i]