Information on Result #1016069
Linear OOA(9114, 7983980, F9, 3, 11) (dual of [(7983980, 3), 23951826, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(932, 2391578, F9, 3, 5) (dual of [(2391578, 3), 7174702, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(932, 2391579, F9, 2, 5) (dual of [(2391579, 2), 4783126, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- Hamming code H(3,9) [i]
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- linear OOA(929, 2391488, F9, 2, 5) (dual of [(2391488, 2), 4782947, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(929, 4782969, F9, 5) (dual of [4782969, 4782940, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(932, 2391579, F9, 2, 5) (dual of [(2391579, 2), 4783126, 6]-NRT-code), using
- linear OOA(982, 5592402, F9, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(8141, 2796201, F81, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(8141, 2796201, F81, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-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(9114, 3991989, F9, 15, 11) (dual of [(3991989, 15), 59879721, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |