MinT - Information on Result #898310

Information on Result #898310

Linear OOA(16⁵⁶, 65555, F₁₆, 2, 13) (dual of [(65555, 2), 131054, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16⁶, 17, F₁₆, 2, 6) (dual of [(17, 2), 28, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;28,16) [i]
linear OOA(16⁵⁰, 65538, F₁₆, 2, 13) (dual of [(65538, 2), 131026, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁵⁰, 131076, F₁₆, 13) (dual of [131076, 131026, 14]-code), using
  - trace code [i] based on linear OA(256²⁵, 65538, F₂₅₆, 13) (dual of [65538, 65513, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(256²⁵, 65536, F₂₅₆, 13) (dual of [65536, 65511, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(256²³, 65536, F₂₅₆, 12) (dual of [65536, 65513, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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(16⁵⁶, 21851, F₁₆, 14, 13) (dual of [(21851, 14), 305858, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row