MinT - Information on Result #898315

Information on Result #898315

Linear OOA(16⁶⁷, 524307, F₁₆, 2, 13) (dual of [(524307, 2), 1048547, 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(16⁶¹, 524290, F₁₆, 2, 13) (dual of [(524290, 2), 1048519, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁶¹, 1048580, F₁₆, 13) (dual of [1048580, 1048519, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁶¹, 1048581, F₁₆, 13) (dual of [1048581, 1048520, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(16⁶¹, 1048576, F₁₆, 13) (dual of [1048576, 1048515, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(16⁵⁶, 1048576, F₁₆, 12) (dual of [1048576, 1048520, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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(16⁶⁷, 174768, F₁₆, 14, 13) (dual of [(174768, 14), 2446685, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row