MinT - Information on Result #1449032

Information on Result #1449032

Linear OOA(9²³, 116658, F₉, 2, 5) (dual of [(116658, 2), 233293, 6]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(9²³, 116658, F₉, 5) (dual of [116658, 116635, 6]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(9⁰, 12962, F₉, 0) (dual of [12962, 12962, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]
2. linear OA(9⁰, 12962, F₉, 0) (dual of [12962, 12962, 1]-code) (see above)
3. linear OA(9⁰, 12962, F₉, 0) (dual of [12962, 12962, 1]-code) (see above)
4. linear OA(9⁰, 12962, F₉, 0) (dual of [12962, 12962, 1]-code) (see above)
5. linear OA(9¹, 12962, F₉, 1) (dual of [12962, 12961, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
6. linear OA(9¹, 12962, F₉, 1) (dual of [12962, 12961, 2]-code) (see above)
7. linear OA(9¹, 12962, F₉, 1) (dual of [12962, 12961, 2]-code) (see above)
8. linear OA(9⁶, 12962, F₉, 2) (dual of [12962, 12956, 3]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁶, 59049, F₉, 2) (dual of [59049, 59043, 3]-code), using
    - an extension C_e(1) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
9. linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
  - trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
    - a code by Danev and Olsson [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9²³, 116657, F₉, 3, 5) (dual of [(116657, 3), 349948, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(9²³, 116657, F₉, 6, 5) (dual of [(116657, 6), 699919, 6]-NRT-code)	[i]		OOA Stacking with Additional Row