MinT - Information on Result #903901

Information on Result #903901

Linear OOA(64⁷¹, 131138, F₆₄, 2, 21) (dual of [(131138, 2), 262205, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁰, 65, F₆₄, 2, 10) (dual of [(65, 2), 120, 11]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;120,64) [i]
linear OOA(64⁶¹, 131073, F₆₄, 2, 21) (dual of [(131073, 2), 262085, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁶¹, 262146, F₆₄, 21) (dual of [262146, 262085, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁶¹, 262147, F₆₄, 21) (dual of [262147, 262086, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
      1. linear OA(64⁶¹, 262144, F₆₄, 21) (dual of [262144, 262083, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(64⁵⁸, 262144, F₆₄, 20) (dual of [262144, 262086, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(64⁷¹, 26227, F₆₄, 22, 21) (dual of [(26227, 22), 576923, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row