About the Z 4 - linear Reed - Muller ZRM − ( r , m − 1 ) and RM s ( r , m ) codes ?
نویسندگان
چکیده
Several different families of quaternary codes related to Reed-Muller binary linear codes can be found in the literature. Two definitions of such families are denoted as ZRM−(r,m) and {RMs(r,m)}. In the current paper ZRM−(r,m− 1) and {RMs(r,m)} codes are shown to be equal exactly for s = 0 (0 ≤ s ≤ bm−1 2 c). Therefore, for the above-mentioned value of s, Z4-linear Reed-Muller codes with the same parameters and properties as the usual binary linear Reed-Muller code are obtained with both definitions.
منابع مشابه
On ZRM codes
Quaternary Z RM (r,m) codes were defined to study theZ4-linearity of ReedMuller codes. In the literature two different definitions of such codes can be found, denoted Z RM (r,m) and Z RM ∗(r,m). We will show that both definitions are equivalent exactly for those values of r such that their binary images are Reed-Muller codes. We will compute the rank and the kernel of their binary image.
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