Information on Result #1442911
Linear OOA(7107, 823587, F7, 2, 17) (dual of [(823587, 2), 1647067, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7107, 823587, F7, 17) (dual of [823587, 823480, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7106, 823585, F7, 17) (dual of [823585, 823479, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(799, 823543, F7, 17) (dual of [823543, 823444, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(77, 42, F7, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(7106, 823586, F7, 16) (dual of [823586, 823480, 17]-code), using Gilbert–Varšamov bound and bm = 7106 > Vbs−1(k−1) = 19558 768963 502016 675470 689029 511988 155399 153640 519766 974892 797012 271754 707932 138040 329479 [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
- linear OA(7106, 823585, F7, 17) (dual of [823585, 823479, 18]-code), 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7107, 411793, F7, 3, 17) (dual of [(411793, 3), 1235272, 18]-NRT-code) | [i] | OOA Folding | |