MinT - Information on Result #902247

Information on Result #902247

Linear OOA(32⁶⁸, 16418, F₃₂, 2, 20) (dual of [(16418, 2), 32768, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁰, 33, F₃₂, 2, 10) (dual of [(33, 2), 56, 11]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;56,32) [i]
linear OOA(32⁵⁸, 16385, F₃₂, 2, 20) (dual of [(16385, 2), 32712, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁵⁸, 32770, F₃₂, 20) (dual of [32770, 32712, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁵⁸, 32771, F₃₂, 20) (dual of [32771, 32713, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(32⁵⁸, 32768, F₃₂, 20) (dual of [32768, 32710, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(32⁵⁵, 32768, F₃₂, 19) (dual of [32768, 32713, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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(32⁶⁸, 3283, F₃₂, 22, 20) (dual of [(3283, 22), 72158, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row