MinT - Information on Result #896253

Information on Result #896253

Linear OOA(7²⁸, 117660, F₇, 2, 5) (dual of [(117660, 2), 235292, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7², 8, F₇, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;14,7) [i]
linear OOA(7²⁶, 117652, F₇, 2, 5) (dual of [(117652, 2), 235278, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7²⁶, 235304, F₇, 5) (dual of [235304, 235278, 6]-code), using
  - trace code [i] based on linear OA(49¹³, 117652, F₄₉, 5) (dual of [117652, 117639, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(49¹³, 117649, F₄₉, 5) (dual of [117649, 117636, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(49¹⁰, 117649, F₄₉, 4) (dual of [117649, 117639, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(49⁰, 3, F₄₉, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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(7²⁸, 117659, F₇, 3, 5) (dual of [(117659, 3), 352949, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(7²⁸, 117659, F₇, 6, 5) (dual of [(117659, 6), 705926, 6]-NRT-code)	[i]		OOA Stacking with Additional Row