Information on Result #902109
Linear OOA(32108, 4718598, F32, 2, 16) (dual of [(4718598, 2), 9437088, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3232, 524297, F32, 2, 8) (dual of [(524297, 2), 1048562, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3232, 1048594, F32, 8) (dual of [1048594, 1048562, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3232, 1048595, F32, 8) (dual of [1048595, 1048563, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [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(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(3232, 1048595, F32, 8) (dual of [1048595, 1048563, 9]-code), using
- OOA 2-folding [i] based on linear OA(3232, 1048594, F32, 8) (dual of [1048594, 1048562, 9]-code), using
- 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(32108, 1179649, F32, 18, 16) (dual of [(1179649, 18), 21233574, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |