Information on Result #1302064
Linear OA(757, 67, F7, 40) (dual of [67, 10, 41]-code), using construction X with Varšamov bound based on
- linear OA(753, 62, F7, 40) (dual of [62, 9, 41]-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(77, 12, F7, 6) (dual of [12, 5, 7]-code), using
- discarding factors / shortening the dual code based on 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 Ce(39) ⊂ Ce(32) ⊂ Ce(31) [i] based on
- linear OA(753, 63, F7, 36) (dual of [63, 10, 37]-code), using Gilbert–Varšamov bound and bm = 753 > Vbs−1(k−1) = 604 876672 510544 512084 195928 702527 302312 570577 [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.