MinT - Information on Result #1832229

Information on Result #1832229

OOA(64⁴⁹, 4227198, S₆₄, 2, 10), using (u,Â u+v)-construction based on

OOA(64¹², 32897, S₆₄, 2, 5), using
- extracting embedded OOA [i] based on (7, 12, 32897)-net in base 64, using
  - base change [i] based on digital (4, 9, 32897)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁹, 32897, F₂₅₆, 5, 5) (dual of [(32897, 5), 164476, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(256⁹, 32897, F₂₅₆, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(256², 257, F₂₅₆, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1026,256) [i]
        linear OOA(256⁷, 32640, F₂₅₆, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(64³⁷, 4194301, F₆₄, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64³⁷, 8388602, F₆₄, 10) (dual of [8388602, 8388565, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OOA(32⁵⁹, 4227198, S₃₂, 2, 10)	[i]		Discarding Parts of the Base for OOAs