Information on Result #806216
Linear OOA(293, 523, F2, 2, 18) (dual of [(523, 2), 953, 19]-NRT-code), using OOA 2-folding 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)
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(293, 410, F2, 3, 18) (dual of [(410, 3), 1137, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(293, 410, F2, 4, 18) (dual of [(410, 4), 1547, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(293, 410, F2, 5, 18) (dual of [(410, 5), 1957, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(293, 410, F2, 6, 18) (dual of [(410, 6), 2367, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(293, 410, F2, 7, 18) (dual of [(410, 7), 2777, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(293, 410, F2, 8, 18) (dual of [(410, 8), 3187, 19]-NRT-code) | [i] | ||
| 7 | Digital (75, 93, 410)-net over F2 | [i] | ||