Information on Result #1297711
Linear OA(2250, 577, F2, 54) (dual of [577, 327, 55]-code), using construction X with Varšamov bound based on
- linear OA(2244, 566, F2, 55) (dual of [566, 322, 56]-code), using
- adding a parity check bit [i] based on linear OA(2243, 565, F2, 54) (dual of [565, 322, 55]-code), using
- construction XX applied to C1 = C([461,510]), C2 = C([467,4]), C3 = C1 + C2 = C([467,510]), and C∩ = C1 ∩ C2 = C([461,4]) [i] based on
- linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,−1}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,4}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,4}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2189, 511, F2, 44) (dual of [511, 322, 45]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,−1}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction XX applied to C1 = C([461,510]), C2 = C([467,4]), C3 = C1 + C2 = C([467,510]), and C∩ = C1 ∩ C2 = C([461,4]) [i] based on
- adding a parity check bit [i] based on linear OA(2243, 565, F2, 54) (dual of [565, 322, 55]-code), using
- linear OA(2244, 571, F2, 52) (dual of [571, 327, 53]-code), using Gilbert–Varšamov bound and bm = 2244 > Vbs−1(k−1) = 25 247225 618692 937810 639496 162454 016024 453950 107186 194651 338373 978083 665464 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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
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
None.