Information on Result #1175751
Linear OOA(2222, 1048707, F2, 8, 16) (dual of [(1048707, 8), 8389434, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(238, 132, F2, 8, 8) (dual of [(132, 8), 1018, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(238, 528, F2, 8) (dual of [528, 490, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(238, 530, F2, 8) (dual of [530, 492, 9]-code), using
- 1 times truncation [i] based on linear OA(239, 531, F2, 9) (dual of [531, 492, 10]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(219, 511, F2, 5) (dual of [511, 492, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- 1 times truncation [i] based on linear OA(239, 531, F2, 9) (dual of [531, 492, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(238, 530, F2, 8) (dual of [530, 492, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(238, 528, F2, 8) (dual of [528, 490, 9]-code), using
- linear OOA(2184, 1048575, F2, 8, 16) (dual of [(1048575, 8), 8388416, 17]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 8-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 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(2222, 1048706, F2, 24, 16) (dual of [(1048706, 24), 25168722, 17]-NRT-code) | [i] | OOA Stacking with Additional Row | |