Information on Result #1509340
Linear OOA(254, 523, F2, 3, 10) (dual of [(523, 3), 1515, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(254, 523, F2, 2, 10) (dual of [(523, 2), 992, 11]-NRT-code), using
- strength reduction [i] based on linear OOA(254, 523, F2, 2, 11) (dual of [(523, 2), 992, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(254, 1046, F2, 11) (dual of [1046, 992, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(254, 1047, F2, 11) (dual of [1047, 993, 12]-code), using
- adding a parity check bit [i] based on linear OA(253, 1046, F2, 10) (dual of [1046, 993, 11]-code), using
- construction XX applied to C1 = C([1021,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([1021,8]) [i] based on
- linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(240, 1023, F2, 8) (dual of [1023, 983, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(230, 1023, F2, 6) (dual of [1023, 993, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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([1021,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([1021,8]) [i] based on
- adding a parity check bit [i] based on linear OA(253, 1046, F2, 10) (dual of [1046, 993, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(254, 1047, F2, 11) (dual of [1047, 993, 12]-code), using
- OOA 2-folding [i] based on linear OA(254, 1046, F2, 11) (dual of [1046, 992, 12]-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(254, 261, F2, 5, 10) (dual of [(261, 5), 1251, 11]-NRT-code) | [i] | OOA Folding | |