MinT - Information on Result #734990

Information on Result #734990

Linear OA(64⁷³, 262277, F₆₄, 20) (dual of [262277, 262204, 21]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁵, 130, F₆₄, 10) (dual of [130, 115, 11]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(64⁵, 65, F₆₄, 5) (dual of [65, 60, 6]-code or 65-arc in PG(4,64)), using
    - extended Reedâ€“Solomon code RS_e(60,64) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
  2. linear OA(64¹⁰, 65, F₆₄, 10) (dual of [65, 55, 11]-code or 65-arc in PG(9,64)), using
    - extended Reedâ€“Solomon code RS_e(55,64) [i]
linear OA(64⁵⁸, 262147, F₆₄, 20) (dual of [262147, 262089, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
  1. 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]
  2. linear OA(64⁵⁵, 262144, F₆₄, 19) (dual of [262144, 262089, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.

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(64⁷³, 131138, F₆₄, 2, 20) (dual of [(131138, 2), 262203, 21]-NRT-code)	[i]		OOA Folding
2	Linear OOA(64⁷³, 87425, F₆₄, 3, 20) (dual of [(87425, 3), 262202, 21]-NRT-code)	[i]		OOA Folding