Information on Result #731022
Linear OA(732, 235304, F7, 6) (dual of [235304, 235272, 7]-code), using trace code based on linear OA(4916, 117652, F49, 6) (dual of [117652, 117636, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4913, 117649, F49, 5) (dual of [117649, 117636, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(733, 235305, F7, 6) (dual of [235305, 235272, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(732, 235304, F7, 2, 6) (dual of [(235304, 2), 470576, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(732, 235304, F7, 3, 6) (dual of [(235304, 3), 705880, 7]-NRT-code) | [i] | ||
| 4 | Digital (26, 32, 235304)-net over F7 | [i] | ||
| 5 | Linear OA(733, 235306, F7, 6) (dual of [235306, 235273, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(732, 117652, F7, 2, 6) (dual of [(117652, 2), 235272, 7]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(732, 78434, F7, 3, 6) (dual of [(78434, 3), 235270, 7]-NRT-code) | [i] | ||
| 8 | Linear OOA(732, 78434, F7, 6, 6) (dual of [(78434, 6), 470572, 7]-NRT-code) | [i] | OA Folding and Stacking | |