Information on Result #684590

Linear OA(7104, 823570, F7, 17) (dual of [823570, 823466, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) based on
  1. linear OA(799, 823543, F7, 17) (dual of [823543, 823444, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  4. linear OA(74, 26, F7, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,7)), using
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-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 OOA(7104, 680168, F7, 2, 17) (dual of [(680168, 2), 1360232, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(7104, 680168, F7, 3, 17) (dual of [(680168, 3), 2040400, 18]-NRT-code) [i]
3Digital (87, 104, 680168)-net over F7 [i]
4Linear OOA(7104, 411785, F7, 2, 17) (dual of [(411785, 2), 823466, 18]-NRT-code) [i]OOA Folding
5Linear OOA(7104, 274523, F7, 3, 17) (dual of [(274523, 3), 823465, 18]-NRT-code) [i]
6Linear OOA(7104, 102946, F7, 17, 17) (dual of [(102946, 17), 1749978, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row