Information on Result #1299705
Linear OA(431, 16395, F4, 6) (dual of [16395, 16364, 7]-code), using construction X with Varšamov bound based on
- linear OA(429, 16391, F4, 6) (dual of [16391, 16362, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(429, 16384, F4, 6) (dual of [16384, 16355, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(429, 16393, F4, 5) (dual of [16393, 16364, 6]-code), using Gilbert–Varšamov bound and bm = 429 > Vbs−1(k−1) = 243600 353713 024291 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s (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(431, 16395, F4, 2, 6) (dual of [(16395, 2), 32759, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(431, 16395, F4, 3, 6) (dual of [(16395, 3), 49154, 7]-NRT-code) | [i] | ||
| 3 | Digital (25, 31, 16395)-net over F4 | [i] | ||