Information on Result #1568407
Linear OOA(2247, 2796435, F2, 3, 18) (dual of [(2796435, 3), 8389058, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(240, 234, F2, 3, 9) (dual of [(234, 3), 662, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 234, F2, 2, 9) (dual of [(234, 2), 428, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 266, F2, 2, 9) (dual of [(266, 2), 492, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 532, F2, 9) (dual of [532, 492, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(240, 533, F2, 9) (dual of [533, 493, 10]-code), using
- adding a parity check bit [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), 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(227, 511, F2, 6) (dual of [511, 484, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(218, 511, F2, 4) (dual of [511, 493, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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, 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 (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- adding a parity check bit [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(240, 533, F2, 9) (dual of [533, 493, 10]-code), using
- OOA 2-folding [i] based on linear OA(240, 532, F2, 9) (dual of [532, 492, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 266, F2, 2, 9) (dual of [(266, 2), 492, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 234, F2, 2, 9) (dual of [(234, 2), 428, 10]-NRT-code), using
- linear OOA(2207, 2796201, F2, 3, 18) (dual of [(2796201, 3), 8388396, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.