Information on Result #1302037
Linear OA(750, 68, F7, 31) (dual of [68, 18, 32]-code), using construction X with Varšamov bound based on
- linear OA(749, 66, F7, 31) (dual of [66, 17, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(747, 63, F7, 31) (dual of [63, 16, 32]-code), using
- construction XX applied to C([1,63]) ⊂ C([1,49]) ⊂ C([1,47]) [i] based on
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(732, 48, F7, 23) (dual of [48, 16, 24]-code), using contraction [i] based on linear OA(780, 96, F7, 47) (dual of [96, 16, 48]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(77, 14, F7, 6) (dual of [14, 7, 7]-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 C([1,63]) ⊂ C([1,49]) ⊂ C([1,47]) [i] based on
- linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code), using Gilbert–Varšamov bound and bm = 747 > Vbs−1(k−1) = 4434 205012 424275 033315 499248 121661 802423 [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 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
- linear OA(747, 63, F7, 31) (dual of [63, 16, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(749, 67, F7, 30) (dual of [67, 18, 31]-code), using Gilbert–Varšamov bound and bm = 749 > Vbs−1(k−1) = 188596 824915 767774 332314 209647 662674 843185 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.