MinT - Information on Result #901776

Information on Result #901776

Linear OOA(32¹⁹, 524323, F₃₂, 2, 5) (dual of [(524323, 2), 1048627, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
linear OOA(32¹⁷, 524290, F₃₂, 2, 5) (dual of [(524290, 2), 1048563, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 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		Method
1	Linear OOA(32⁶⁵, 4718624, F₃₂, 2, 10) (dual of [(4718624, 2), 9437183, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁷⁰, 4718624, F₃₂, 2, 11) (dual of [(4718624, 2), 9437178, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(32¹⁹, 524322, F₃₂, 6, 5) (dual of [(524322, 6), 3145913, 6]-NRT-code)	[i]	OOA Stacking with Additional Row