Information on Result #685097
Linear OA(763, 2412, F7, 18) (dual of [2412, 2349, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(14) based on
- linear OA(761, 2401, F7, 18) (dual of [2401, 2340, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(753, 2401, F7, 16) (dual of [2401, 2348, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(749, 2401, F7, 15) (dual of [2401, 2352, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(71, 10, F7, 1) (dual of [10, 9, 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(763, 2124, F7, 2, 18) (dual of [(2124, 2), 4185, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 2124, F7, 3, 18) (dual of [(2124, 3), 6309, 19]-NRT-code) | [i] | ||
| 3 | Digital (45, 63, 2124)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 1206, F7, 2, 18) (dual of [(1206, 2), 2349, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(763, 804, F7, 3, 18) (dual of [(804, 3), 2349, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(763, 268, F7, 18, 18) (dual of [(268, 18), 4761, 19]-NRT-code) | [i] | OA Folding and Stacking | |