Information on Result #900769
Linear OOA(27107, 4204172, F27, 2, 17) (dual of [(4204172, 2), 8408237, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2726, 9871, F27, 2, 8) (dual of [(9871, 2), 19716, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(274, 28, F27, 2, 4) (dual of [(28, 2), 52, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;52,27) [i]
- linear OOA(2722, 9843, F27, 2, 8) (dual of [(9843, 2), 19664, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2719, 19683, F27, 7) (dual of [19683, 19664, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- linear OOA(274, 28, F27, 2, 4) (dual of [(28, 2), 52, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2781, 4194301, F27, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(27107, 1051042, F27, 18, 17) (dual of [(1051042, 18), 18918649, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |