MinT - Information on Result #1017329

Information on Result #1017329

Linear OOA(49⁵⁵, 1921651, F₄₉, 3, 13) (dual of [(1921651, 3), 5764898, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49⁶, 50, F₄₉, 3, 6) (dual of [(50, 3), 144, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;144,49) [i]
linear OOA(49⁴⁹, 1921601, F₄₉, 3, 13) (dual of [(1921601, 3), 5764754, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49⁴⁹, 5764803, F₄₉, 13) (dual of [5764803, 5764754, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁴⁹, 5764805, F₄₉, 13) (dual of [5764805, 5764756, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(49⁴⁹, 5764801, F₄₉, 13) (dual of [5764801, 5764752, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 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(49⁵⁵, 960825, F₄₉, 15, 13) (dual of [(960825, 15), 14412320, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row