MinT - Information on Result #1018140

Information on Result #1018140

Linear OOA(64⁸², 87447, F₆₄, 3, 24) (dual of [(87447, 3), 262259, 25]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹², 65, F₆₄, 3, 12) (dual of [(65, 3), 183, 13]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;183,64) [i]
linear OOA(64⁷⁰, 87382, F₆₄, 3, 24) (dual of [(87382, 3), 262076, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁷⁰, 262146, F₆₄, 24) (dual of [262146, 262076, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁷⁰, 262147, F₆₄, 24) (dual of [262147, 262077, 25]-code), using
    - constructionÂ X applied to C_e(23) âŠ‚ C_e(22) [i] based on
      1. linear OA(64⁷⁰, 262144, F₆₄, 24) (dual of [262144, 262074, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
      2. linear OA(64⁶⁷, 262144, F₆₄, 23) (dual of [262144, 262077, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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(64⁸², 21861, F₆₄, 27, 24) (dual of [(21861, 27), 590165, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row