Information on Result #902110
Linear OOA(32109, 4718624, F32, 2, 16) (dual of [(4718624, 2), 9437139, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3233, 524323, F32, 2, 8) (dual of [(524323, 2), 1048613, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;62,32) [i]
- linear OOA(3229, 524290, F32, 2, 8) (dual of [(524290, 2), 1048551, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 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(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- linear OOA(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3276, 4194301, F32, 2, 16) (dual of [(4194301, 2), 8388526, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3276, 8388602, F32, 16) (dual of [8388602, 8388526, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- OOA 2-folding [i] based on linear OA(3276, 8388602, F32, 16) (dual of [8388602, 8388526, 17]-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(32109, 1179655, F32, 18, 16) (dual of [(1179655, 18), 21233681, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |