Information on Result #680935
Linear OA(4248, 1106, F4, 58) (dual of [1106, 858, 59]-code), using construction X applied to Ce(57) ⊂ Ce(44) based on
- linear OA(4216, 1024, F4, 58) (dual of [1024, 808, 59]-code), using an extension Ce(57) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,57], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(4166, 1024, F4, 45) (dual of [1024, 858, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(432, 82, F4, 12) (dual of [82, 50, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(432, 90, F4, 12) (dual of [90, 58, 13]-code), using
- trace code [i] based on linear OA(1616, 45, F16, 12) (dual of [45, 29, 13]-code), using
- extended algebraic-geometric code AGe(F,32P) [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- trace code [i] based on linear OA(1616, 45, F16, 12) (dual of [45, 29, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(432, 90, F4, 12) (dual of [90, 58, 13]-code), 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(4249, 1107, F4, 58) (dual of [1107, 858, 59]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4250, 1108, F4, 58) (dual of [1108, 858, 59]-code) | [i] | ||
| 3 | Linear OA(4251, 1109, F4, 58) (dual of [1109, 858, 59]-code) | [i] | ||
| 4 | Linear OOA(4248, 553, F4, 2, 58) (dual of [(553, 2), 858, 59]-NRT-code) | [i] | OOA Folding | |