MinT - Information on Result #897392

Information on Result #897392

Linear OOA(9²⁸, 531454, F₉, 2, 5) (dual of [(531454, 2), 1062880, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9², 10, F₉, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;18,9) [i]
linear OOA(9²⁶, 531444, F₉, 2, 5) (dual of [(531444, 2), 1062862, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9²⁶, 1062888, F₉, 5) (dual of [1062888, 1062862, 6]-code), using
  - trace code [i] based on linear OA(81¹³, 531444, F₈₁, 5) (dual of [531444, 531431, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(81¹³, 531441, F₈₁, 5) (dual of [531441, 531428, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(81¹⁰, 531441, F₈₁, 4) (dual of [531441, 531431, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9²⁸, 531453, F₉, 3, 5) (dual of [(531453, 3), 1594331, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(9²⁸, 531453, F₉, 6, 5) (dual of [(531453, 6), 3188690, 6]-NRT-code)	[i]		OOA Stacking with Additional Row