Information on Result #1016132
Linear OOA(987, 1594353, F9, 3, 13) (dual of [(1594353, 3), 4782972, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(99, 28, F9, 3, 6) (dual of [(28, 3), 75, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,77P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- extended algebraic-geometric NRT-code AGe(3;F,77P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- linear OOA(978, 1594325, F9, 3, 13) (dual of [(1594325, 3), 4782897, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(978, 4782975, F9, 13) (dual of [4782975, 4782897, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(978, 4782976, F9, 13) (dual of [4782976, 4782898, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(978, 4782976, F9, 13) (dual of [4782976, 4782898, 14]-code), using
- OOA 3-folding [i] based on linear OA(978, 4782975, F9, 13) (dual of [4782975, 4782897, 14]-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(987, 797176, F9, 15, 13) (dual of [(797176, 15), 11957553, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |