Information on Result #1302056
Linear OA(756, 66, F7, 39) (dual of [66, 10, 40]-code), using construction X with Varšamov bound based on
- linear OA(752, 61, F7, 39) (dual of [61, 9, 40]-code), using
- construction XX applied to Ce(39) ⊂ Ce(32) ⊂ Ce(31) [i] based on
- linear OA(745, 49, F7, 40) (dual of [49, 4, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(741, 49, F7, 33) (dual of [49, 8, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(740, 49, F7, 32) (dual of [49, 9, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(39) ⊂ Ce(32) ⊂ Ce(31) [i] based on
- linear OA(752, 62, F7, 35) (dual of [62, 10, 36]-code), using Gilbert–Varšamov bound and bm = 752 > Vbs−1(k−1) = 56 498727 269929 940922 947437 209967 486615 483495 [i]
- linear OA(73, 4, F7, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,7) or 4-cap in PG(2,7)), using
- dual of repetition code with length 4 [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.