Information on Result #1510394
Linear OOA(2102, 400, F2, 3, 20) (dual of [(400, 3), 1098, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2102, 400, F2, 2, 20) (dual of [(400, 2), 698, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2102, 522, F2, 2, 20) (dual of [(522, 2), 942, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2102, 1044, F2, 20) (dual of [1044, 942, 21]-code), using
- 1 times truncation [i] based on linear OA(2103, 1045, F2, 21) (dual of [1045, 942, 22]-code), using
- construction XX applied to C1 = C([1021,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([1021,18]) [i] based on
- 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(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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, using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([1021,18]) [i] based on
- 1 times truncation [i] based on linear OA(2103, 1045, F2, 21) (dual of [1045, 942, 22]-code), using
- OOA 2-folding [i] based on linear OA(2102, 1044, F2, 20) (dual of [1044, 942, 21]-code), using
Mode: 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(2102, 200, F2, 6, 20) (dual of [(200, 6), 1098, 21]-NRT-code) | [i] | OOA Folding | |