MinT - Information on Result #1017987

Information on Result #1017987

Linear OOA(64⁶³, 87463, F₆₄, 3, 18) (dual of [(87463, 3), 262326, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁰, 80, F₆₄, 3, 9) (dual of [(80, 3), 230, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,230P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
  - a function field by SÃ©mirat [i]
linear OOA(64⁵³, 87383, F₆₄, 3, 18) (dual of [(87383, 3), 262096, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁵³, 262149, F₆₄, 18) (dual of [262149, 262096, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁵³, 262151, F₆₄, 18) (dual of [262151, 262098, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(15) [i] based on
      1. linear OA(64⁵², 262144, F₆₄, 18) (dual of [262144, 262092, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. 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]
      3. linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and 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(64⁶³, 29154, F₆₄, 21, 18) (dual of [(29154, 21), 612171, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row