Information on Result #1709851
Linear OOA(2222, 2097414, F2, 24, 16) (dual of [(2097414, 24), 50337714, 17]-NRT-code), using OOA stacking with additional row based on linear OOA(2222, 2097415, F2, 8, 16) (dual of [(2097415, 8), 16779098, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2222, 2097415, F2, 4, 16) (dual of [(2097415, 4), 8389438, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(238, 265, F2, 4, 8) (dual of [(265, 4), 1022, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 265, F2, 2, 8) (dual of [(265, 2), 492, 9]-NRT-code), using
- OOA 2-folding [i] 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
- OOA 2-folding [i] based on linear OA(238, 530, F2, 8) (dual of [530, 492, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 265, F2, 2, 8) (dual of [(265, 2), 492, 9]-NRT-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-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 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(238, 265, F2, 4, 8) (dual of [(265, 4), 1022, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (206, 222, 2097414)-net over F2 | [i] | Net Defined by OOA | |