MinT - Information on Result #944760

Information on Result #944760

Linear OOA(9³², 2391578, F₉, 3, 5) (dual of [(2391578, 3), 7174702, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(9³², 2391579, F₉, 2, 5) (dual of [(2391579, 2), 4783126, 6]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(9³, 91, F₉, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(9³, 91, F₉, 2) (dual of [91, 88, 3]-code), using
    - Hamming code H(3,9) [i]
2. linear OOA(9²⁹, 2391488, F₉, 2, 5) (dual of [(2391488, 2), 4782947, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9²⁹, 4782976, F₉, 5) (dual of [4782976, 4782947, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(9²⁹, 4782969, F₉, 5) (dual of [4782969, 4782940, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(9²², 4782969, F₉, 4) (dual of [4782969, 4782947, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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]

Mode: Constructive and 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(9¹⁰⁶, 7983980, F₉, 3, 10) (dual of [(7983980, 3), 23951834, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(9¹¹⁴, 7983980, F₉, 3, 11) (dual of [(7983980, 3), 23951826, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs