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In information theory, the bar product of two linear codes is defined as

The bar product is an especially bar code label software free convenient way bar code label bar code printer labels printing of expressing the Reed-Muller RM(d,r) code in terms of the Reed-Muller codes RM(d-1,r-1) bar code label metal and RM(d-1,r).

Properties

Rank

The create bar code labels rank of the bar product is the sum of the two ranks:

rank(C 1 | C 2) bar code labels and nurses = rank(C 1) bar citizen code label printer + rank(C 2)

Proof

Let bar code free label software aiag format bar code labels be a basis for $C 1$ tape bar code label and let be a basis for $C 2$ . Then the set

is a basis for the bar product bar code asset bar bar code label template code label security label $C 1 | C 2$ .

Hamming label printers exabyte bar code label and bar code scranners weight

The lto bar code label upc bar code labels Hamming weight of the bar product is the minimum value of:

w (C 1 bar code labels | C 2) = min{2 w (C 1), w (C 2)}

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Proof

For bar code label printer all c_1 \in C_1,

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which has weight $2 w (c 1)$ . preprinted bar code bar code label scanner bar code scranner, label printing technology labels Equally

for all and has weight $w (c 2)$ . So minimising label view code bar over we have

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Now let and , not both zero. If then:

If $c 2 = 0$ then

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