Information on Result #1019425
Linear OOA(12864, 699243, F128, 3, 18) (dual of [(699243, 3), 2097665, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12812, 192, F128, 3, 9) (dual of [(192, 3), 564, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,566P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OOA(12852, 699051, F128, 3, 18) (dual of [(699051, 3), 2097101, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- OOA 3-folding [i] based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-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 OOA(12864, 233080, F128, 21, 18) (dual of [(233080, 21), 4894616, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |