MinT - Information on Result #1017159

Information on Result #1017159

Linear OOA(49¹⁹, 39267, F₄₉, 3, 6) (dual of [(39267, 3), 117782, 7]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49³, 50, F₄₉, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;147,49) [i]
linear OOA(49¹⁶, 39217, F₄₉, 3, 6) (dual of [(39217, 3), 117635, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49¹⁶, 117651, F₄₉, 6) (dual of [117651, 117635, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(49¹⁶, 117652, F₄₉, 6) (dual of [117652, 117636, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(49¹⁶, 117649, F₄₉, 6) (dual of [117649, 117633, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. 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]
      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(49¹⁹, 39266, F₄₉, 9, 6) (dual of [(39266, 9), 353375, 7]-NRT-code)	[i]		OOA Stacking with Additional Row