MinT - Information on Result #901802

Information on Result #901802

Linear OOA(32²², 16418, F₃₂, 2, 7) (dual of [(16418, 2), 32814, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32³, 33, F₃₂, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;63,32) [i]
linear OOA(32¹⁹, 16385, F₃₂, 2, 7) (dual of [(16385, 2), 32751, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁹, 32770, F₃₂, 7) (dual of [32770, 32751, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁹, 32771, F₃₂, 7) (dual of [32771, 32752, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
      1. linear OA(32¹⁹, 32768, F₃₂, 7) (dual of [32768, 32749, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(32¹⁶, 32768, F₃₂, 6) (dual of [32768, 32752, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(32⁸⁸, 4210719, F₃₂, 2, 14) (dual of [(4210719, 2), 8421350, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁹³, 4210719, F₃₂, 2, 15) (dual of [(4210719, 2), 8421345, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs