Information on Result #1323886
Linear OA(488, 16430, F4, 15) (dual of [16430, 16342, 16]-code), using construction X with Varšamov bound based on
- linear OA(487, 16428, F4, 15) (dual of [16428, 16341, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(443, 16384, F4, 9) (dual of [16384, 16341, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(487, 16429, F4, 14) (dual of [16429, 16342, 15]-code), using Gilbert–Varšamov bound and bm = 487 > Vbs−1(k−1) = 1617 890494 033576 252032 805439 174497 591533 143535 810904 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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
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(488, 16430, F4, 2, 15) (dual of [(16430, 2), 32772, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(488, 16430, F4, 3, 15) (dual of [(16430, 3), 49202, 16]-NRT-code) | [i] | ||
| 3 | Digital (73, 88, 16430)-net over F4 | [i] | ||
| 4 | Linear OOA(488, 8215, F4, 2, 15) (dual of [(8215, 2), 16342, 16]-NRT-code) | [i] | OOA Folding | |