MinT - Information on Result #735000

Information on Result #735000

Linear OA(64⁵⁰, 4228, F₆₄, 19) (dual of [4228, 4178, 20]-code), using (u,Â u+v)-construction based on

linear OA(64¹³, 130, F₆₄, 9) (dual of [130, 117, 10]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(64⁴, 65, F₆₄, 4) (dual of [65, 61, 5]-code or 65-arc in PG(3,64)), using
    - extended Reedâ€“Solomon code RS_e(61,64) [i]
  2. linear OA(64⁹, 65, F₆₄, 9) (dual of [65, 56, 10]-code or 65-arc in PG(8,64)), using
    - extended Reedâ€“Solomon code RS_e(56,64) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
linear OA(64³⁷, 4098, F₆₄, 19) (dual of [4098, 4061, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
  1. linear OA(64³⁷, 4096, F₆₄, 19) (dual of [4096, 4059, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(64³⁵, 4096, F₆₄, 18) (dual of [4096, 4061, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(64⁵⁰, 2114, F₆₄, 2, 19) (dual of [(2114, 2), 4178, 20]-NRT-code)	[i]		OOA Folding