Information on Result #1710273
Linear OOA(294, 214, F2, 25, 18) (dual of [(214, 25), 5256, 19]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(294, 429, F2, 5, 18) (dual of [(429, 5), 2051, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 430, F2, 5, 18) (dual of [(430, 5), 2056, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(294, 430, F2, 2, 18) (dual of [(430, 2), 766, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 523, F2, 2, 18) (dual of [(523, 2), 952, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(294, 523, F2, 2, 19) (dual of [(523, 2), 952, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(294, 1046, F2, 19) (dual of [1046, 952, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(294, 1047, F2, 19) (dual of [1047, 953, 20]-code), using
- adding a parity check bit [i] based on linear OA(293, 1046, F2, 18) (dual of [1046, 953, 19]-code), using
- construction XX applied to C1 = C([1021,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(270, 1023, F2, 14) (dual of [1023, 953, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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, 11, F2, 1) (dual of [11, 10, 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 (see above)
- construction XX applied to C1 = C([1021,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- adding a parity check bit [i] based on linear OA(293, 1046, F2, 18) (dual of [1046, 953, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(294, 1047, F2, 19) (dual of [1047, 953, 20]-code), using
- OOA 2-folding [i] based on linear OA(294, 1046, F2, 19) (dual of [1046, 952, 20]-code), using
- strength reduction [i] based on linear OOA(294, 523, F2, 2, 19) (dual of [(523, 2), 952, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 523, F2, 2, 18) (dual of [(523, 2), 952, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(294, 430, F2, 2, 18) (dual of [(430, 2), 766, 19]-NRT-code), using
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 (76, 94, 214)-net over F2 | [i] | Net Defined by OOA | |