MinT - Information on Result #902506

Information on Result #902506

Linear OOA(32⁹⁶, 16418, F₃₂, 2, 28) (dual of [(16418, 2), 32740, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁴, 33, F₃₂, 2, 14) (dual of [(33, 2), 52, 15]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;52,32) [i]
linear OOA(32⁸², 16385, F₃₂, 2, 28) (dual of [(16385, 2), 32688, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁸², 32770, F₃₂, 28) (dual of [32770, 32688, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁸², 32771, F₃₂, 28) (dual of [32771, 32689, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
      1. linear OA(32⁸², 32768, F₃₂, 28) (dual of [32768, 32686, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(32⁷⁹, 32768, F₃₂, 27) (dual of [32768, 32689, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(32⁹⁶, 2345, F₃₂, 30, 28) (dual of [(2345, 30), 70254, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row