Information on Result #1443008
Linear OOA(7109, 823591, F7, 2, 17) (dual of [(823591, 2), 1647073, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7109, 823591, F7, 17) (dual of [823591, 823482, 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, 823588, F7, 16) (dual of [823588, 823482, 17]-code), using Gilbert–Varšamov bound and bm = 7106 > Vbs−1(k−1) = 19559 481431 446353 245831 493276 788957 679380 588391 039563 056234 797349 577467 625004 211603 961431 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 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(7109, 411795, F7, 3, 17) (dual of [(411795, 3), 1235276, 18]-NRT-code) | [i] | OOA Folding | |