Information on Result #1313859
Linear OA(1680, 4138, F16, 27) (dual of [4138, 4058, 28]-code), using 32 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 25 times 0) based on linear OA(1677, 4103, F16, 27) (dual of [4103, 4026, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(1676, 4096, F16, 27) (dual of [4096, 4020, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(1670, 4096, F16, 25) (dual of [4096, 4026, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-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(1680, 4138, F16, 2, 27) (dual of [(4138, 2), 8196, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 80, 4138)-net over F16 | [i] | ||
| 3 | Linear OOA(1680, 2069, F16, 2, 27) (dual of [(2069, 2), 4058, 28]-NRT-code) | [i] | OOA Folding | |