MinT - Information on Result #900528

Information on Result #900528

Linear OOA(27⁵¹, 265750, F₂₇, 2, 12) (dual of [(265750, 2), 531449, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27⁶, 28, F₂₇, 2, 6) (dual of [(28, 2), 50, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;50,27) [i]
linear OOA(27⁴⁵, 265722, F₂₇, 2, 12) (dual of [(265722, 2), 531399, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁴⁵, 531444, F₂₇, 12) (dual of [531444, 531399, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁴⁵, 531445, F₂₇, 12) (dual of [531445, 531400, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(27⁴⁵, 531441, F₂₇, 12) (dual of [531441, 531396, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(27⁴¹, 531441, F₂₇, 11) (dual of [531441, 531400, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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(27⁵¹, 88583, F₂₇, 14, 12) (dual of [(88583, 14), 1240111, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row