MinT - Information on Result #901951

Information on Result #901951

Linear OOA(32⁴³, 16418, F₃₂, 2, 13) (dual of [(16418, 2), 32793, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32⁶, 33, F₃₂, 2, 6) (dual of [(33, 2), 60, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;60,32) [i]
linear OOA(32³⁷, 16385, F₃₂, 2, 13) (dual of [(16385, 2), 32733, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32³⁷, 32770, F₃₂, 13) (dual of [32770, 32733, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(32³⁷, 32771, F₃₂, 13) (dual of [32771, 32734, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(32³⁷, 32768, F₃₂, 13) (dual of [32768, 32731, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(32³⁴, 32768, F₃₂, 12) (dual of [32768, 32734, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(32⁴³, 5472, F₃₂, 14, 13) (dual of [(5472, 14), 76565, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row