MinT - Information on Result #734956

Information on Result #734956

Linear OA(64⁵⁶, 4228, F₆₄, 21) (dual of [4228, 4172, 22]-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(64⁴¹, 4098, F₆₄, 21) (dual of [4098, 4057, 22]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
  1. linear OA(64⁴¹, 4096, F₆₄, 21) (dual of [4096, 4055, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  2. 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]
  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(64⁵⁶, 2114, F₆₄, 2, 21) (dual of [(2114, 2), 4172, 22]-NRT-code)	[i]		OOA Folding