MinT - Information on Result #1564328

Information on Result #1564328

Linear OOA(64⁴², 2017, F₆₄, 3, 20) (dual of [(2017, 3), 6009, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁴², 2017, F₆₄, 2, 20) (dual of [(2017, 2), 3992, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁴², 2053, F₆₄, 2, 20) (dual of [(2053, 2), 4064, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴², 4106, F₆₄, 20) (dual of [4106, 4064, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴², 4107, F₆₄, 20) (dual of [4107, 4065, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(15) [i] based on
      1. linear OA(64³⁹, 4096, F₆₄, 20) (dual of [4096, 4057, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(64³¹, 4096, F₆₄, 16) (dual of [4096, 4065, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(64³, 11, F₆₄, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
        discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁴², 504, F₆₄, 27, 20) (dual of [(504, 27), 13566, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row