MinT - Information on Result #903753

Information on Result #903753

Linear OOA(64⁵⁴, 131138, F₆₄, 2, 16) (dual of [(131138, 2), 262222, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64⁸, 65, F₆₄, 2, 8) (dual of [(65, 2), 122, 9]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;122,64) [i]
linear OOA(64⁴⁶, 131073, F₆₄, 2, 16) (dual of [(131073, 2), 262100, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴⁶, 262146, F₆₄, 16) (dual of [262146, 262100, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴⁶, 262147, F₆₄, 16) (dual of [262147, 262101, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
      1. linear OA(64⁴⁶, 262144, F₆₄, 16) (dual of [262144, 262098, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(64⁴³, 262144, F₆₄, 15) (dual of [262144, 262101, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(64⁵⁴, 32784, F₆₄, 18, 16) (dual of [(32784, 18), 590058, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row