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Table 2 Syndromes for ECC generator

From: Error-correcting properties of the SOLiD Exact Call Chemistry

Error

Interpretation

Position

   

Equivalence

Type

 

p

c 1

c 2

c 3

c 4

c 5

p +

   

classes

+ β

Complement

β 0

0β

α 1

α 1

0β

ββ

0β

   

{c 5}

+ α

Transition

α 0

0α

1β

1β

0α

αα

0α

   

{c 2,c 3}

+1

Transcomplement

10

01

βα

βα

01

11

01

   

{c 1,c 4,p +}

  1. All syndromes caused by a single error in a block of five code letters (c 1c 2c 3c 4c 5) and two parity letters (pp +) of the SOLiD ECC code. Each row in the table corresponds to a specific type of error at the given position of the code word, with the ‘interpretation’ of an error type being the effect it would have when considered as a nucleotide substitution. The table entries are the values of the relevant elements of the syndrome, corresponding to the upstream and downstream parity checks for the block for each error type. The error type +0 is not shown since it represents no error; its syndromes would be 00 at all positions. The equivalence classes are listed separately and do not correspond to specific error types. Note that pis also p +for the preceding block.