MinT - Information on Result #900745

Information on Result #900745

Linear OOA(27⁷³, 265750, F₂₇, 2, 17) (dual of [(265750, 2), 531427, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27⁸, 28, F₂₇, 2, 8) (dual of [(28, 2), 48, 9]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;48,27) [i]
linear OOA(27⁶⁵, 265722, F₂₇, 2, 17) (dual of [(265722, 2), 531379, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁶⁵, 531444, F₂₇, 17) (dual of [531444, 531379, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁶⁵, 531445, F₂₇, 17) (dual of [531445, 531380, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
      1. linear OA(27⁶⁵, 531441, F₂₇, 17) (dual of [531441, 531376, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(27⁶¹, 531441, F₂₇, 16) (dual of [531441, 531380, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(27⁷³, 66437, F₂₇, 18, 17) (dual of [(66437, 18), 1195793, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row