Information on Result #680005
Linear OA(475, 4111, F4, 16) (dual of [4111, 4036, 17]-code), using construction XX applied to Ce(16) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(473, 4096, F4, 17) (dual of [4096, 4023, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(461, 4096, F4, 14) (dual of [4096, 4035, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(455, 4096, F4, 13) (dual of [4096, 4041, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(475, 3056, F4, 2, 16) (dual of [(3056, 2), 6037, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(475, 3056, F4, 3, 16) (dual of [(3056, 3), 9093, 17]-NRT-code) | [i] | ||
| 3 | Digital (59, 75, 3056)-net over F4 | [i] | ||
| 4 | Linear OOA(475, 2055, F4, 2, 16) (dual of [(2055, 2), 4035, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(475, 1370, F4, 3, 16) (dual of [(1370, 3), 4035, 17]-NRT-code) | [i] | ||