Information on Result #1308236
Linear OA(4165, 4177, F4, 35) (dual of [4177, 4012, 36]-code), using 67 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0) based on linear OA(4157, 4102, F4, 35) (dual of [4102, 3945, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(33) [i] based on
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(4165, 4177, F4, 2, 35) (dual of [(4177, 2), 8189, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4165, 4177, F4, 3, 35) (dual of [(4177, 3), 12366, 36]-NRT-code) | [i] | ||
| 3 | Digital (130, 165, 4177)-net over F4 | [i] | ||
| 4 | Linear OOA(4165, 2088, F4, 2, 35) (dual of [(2088, 2), 4011, 36]-NRT-code) | [i] | OOA Folding | |