Information on Result #679103
Linear OA(444, 16400, F4, 8) (dual of [16400, 16356, 9]-code), using construction X4 applied to Ce(8) ⊂ Ce(5) based on
- 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(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(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-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(445, 16401, F4, 8) (dual of [16401, 16356, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(444, 16400, F4, 2, 8) (dual of [(16400, 2), 32756, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(444, 16400, F4, 3, 8) (dual of [(16400, 3), 49156, 9]-NRT-code) | [i] | ||
| 4 | Digital (36, 44, 16400)-net over F4 | [i] | ||
| 5 | Linear OA(445, 16402, F4, 8) (dual of [16402, 16357, 9]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(444, 8200, F4, 2, 8) (dual of [(8200, 2), 16356, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(444, 4100, F4, 8, 8) (dual of [(4100, 8), 32756, 9]-NRT-code) | [i] | OA Folding and Stacking | |