Information on Result #1311572
Linear OA(748, 406, F7, 17) (dual of [406, 358, 18]-code), using 53 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 6 times 0, 1, 14 times 0, 1, 28 times 0) based on linear OA(743, 348, F7, 17) (dual of [348, 305, 18]-code), using
- construction XX applied to C1 = C([341,14]), C2 = C([0,15]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([341,15]) [i] based on
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
Mode: 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(748, 406, F7, 2, 17) (dual of [(406, 2), 764, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(748, 406, F7, 3, 17) (dual of [(406, 3), 1170, 18]-NRT-code) | [i] | ||
| 3 | Digital (31, 48, 406)-net over F7 | [i] | ||
| 4 | Linear OOA(748, 203, F7, 2, 17) (dual of [(203, 2), 358, 18]-NRT-code) | [i] | OOA Folding | |