MinT - Information on Result #735108

Information on Result #735108

Linear OA(64³², 4228, F₆₄, 12) (dual of [4228, 4196, 13]-code), using (u,Â u+v)-construction based on

linear OA(64⁹, 130, F₆₄, 6) (dual of [130, 121, 7]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(64³, 65, F₆₄, 3) (dual of [65, 62, 4]-code or 65-arc in PG(2,64) or 65-cap in PG(2,64)), using
    - extended Reedâ€“Solomon code RS_e(62,64) [i]
  2. linear OA(64⁶, 65, F₆₄, 6) (dual of [65, 59, 7]-code or 65-arc in PG(5,64)), using
    - extended Reedâ€“Solomon code RS_e(59,64) [i]
linear OA(64²³, 4098, F₆₄, 12) (dual of [4098, 4075, 13]-code), using
- constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
  1. linear OA(64²³, 4096, F₆₄, 12) (dual of [4096, 4073, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  2. linear OA(64²¹, 4096, F₆₄, 11) (dual of [4096, 4075, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 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(64³², 2114, F₆₄, 2, 12) (dual of [(2114, 2), 4196, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(64³², 1409, F₆₄, 3, 12) (dual of [(1409, 3), 4195, 13]-NRT-code)	[i]		OOA Folding