MinT - Information on Result #898218

Information on Result #898218

Linear OOA(16¹⁸, 524307, F₁₆, 2, 4) (dual of [(524307, 2), 1048596, 5]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16², 17, F₁₆, 2, 2) (dual of [(17, 2), 32, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;32,16) [i]
linear OOA(16¹⁶, 524290, F₁₆, 2, 4) (dual of [(524290, 2), 1048564, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹⁶, 1048580, F₁₆, 4) (dual of [1048580, 1048564, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁶, 1048581, F₁₆, 4) (dual of [1048581, 1048565, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(16¹⁶, 1048576, F₁₆, 4) (dual of [1048576, 1048560, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(16¹¹, 1048576, F₁₆, 3) (dual of [1048576, 1048565, 4]-code or 1048576-cap in PG(10,16)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(16¹⁸, 524306, F₁₆, 6, 4) (dual of [(524306, 6), 3145818, 5]-NRT-code)	[i]		OOA Stacking with Additional Row