Information on Result #1297679
Linear OA(2245, 580, F2, 52) (dual of [580, 335, 53]-code), using construction X with Varšamov bound based on
- linear OA(2242, 574, F2, 52) (dual of [574, 332, 53]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2241, 572, F2, 52) (dual of [572, 331, 53]-code), using
- 1 times truncation [i] based on linear OA(2242, 573, F2, 53) (dual of [573, 331, 54]-code), using
- construction X applied to Ce(52) ⊂ Ce(42) [i] based on
- linear OA(2217, 512, F2, 53) (dual of [512, 295, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2181, 512, F2, 43) (dual of [512, 331, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(225, 61, F2, 9) (dual of [61, 36, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), using
- construction X applied to Ce(52) ⊂ Ce(42) [i] based on
- 1 times truncation [i] based on linear OA(2242, 573, F2, 53) (dual of [573, 331, 54]-code), using
- linear OA(2241, 573, F2, 51) (dual of [573, 332, 52]-code), using Gilbert–Varšamov bound and bm = 2241 > Vbs−1(k−1) = 2 965641 449785 938915 833899 821230 013497 105534 728227 912715 749496 089904 246133 [i]
- linear OA(20, 1, F2, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(20, s, F2, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(2241, 572, F2, 52) (dual of [572, 331, 53]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2242, 577, F2, 51) (dual of [577, 335, 52]-code), using Gilbert–Varšamov bound and bm = 2242 > Vbs−1(k−1) = 4 265313 665127 145149 599820 868601 544089 248732 151356 933208 232294 234224 261591 [i]
- linear OA(20, 3, F2, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(20, s, F2, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
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.