Table 4 The usage number of four arithmetic operators per decoding of a single row/column vector required in the error correction of the proposed syndrome-based decoding algorithm (reference to Fig. 1)

No

HISO

n

2n

2n−k

n(n−k)

error

(t=1)

HDD-based

n

3n

n(d+2)−k+1

n(n−k+1)

Single

HISO (t=2)

error

SISO

n(2^p−1+2)

n(2^p−1+3)

2^p−1(2n+3)

(2^p−1−1)(n²−nk+k+p)

(t=3)

+n(d+1)−k−4

+n(n−k+1)

BFHDD-

n

3n

n(d+2)−k−d+5

n(n−k+1)

Double

HISO (t=4)

error

SISO

n(2^p−1+2)

n(2^p−1+3)

2^p−1(2n+3)

(2^p−1−1)(n²−nk+k+p)

(t=5)

+n(d+1)−d−k

+n(n−k+1)