Information on Result #684589
Linear OA(7108, 823560, F7, 18) (dual of [823560, 823452, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(14) based on
- linear OA(7106, 823543, F7, 18) (dual of [823543, 823437, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7108, 508127, F7, 2, 18) (dual of [(508127, 2), 1016146, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7108, 508127, F7, 3, 18) (dual of [(508127, 3), 1524273, 19]-NRT-code) | [i] | ||
| 3 | Digital (90, 108, 508127)-net over F7 | [i] | ||
| 4 | Linear OOA(7108, 411780, F7, 2, 18) (dual of [(411780, 2), 823452, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7108, 274520, F7, 3, 18) (dual of [(274520, 3), 823452, 19]-NRT-code) | [i] | ||