Let C1 and C2 be two linear block codes. Define three new codes (called respectively concatenation,...

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Let C1 and C2 be two linear block codes. Define three new codes (called respectively concatenation, bar product and tensor product codes) as C = {(ci c2) : 1 € C, and cz E C2} D = {(c ci + c2) c1 E C, and cz E C2} E = {c ® c2 : G € C, and cz E C2}. Show that these are also block linear codes and study their properties in terms of those of the original codes. Show in particular that dp = min {2d1, d2} Let C1 and C2 be two linear block codes. Define three new codes (called respectively concatenation, bar product and tensor product codes) as C = {(ci c2) : 1 € C, and cz E C2} D = {(c ci + c2) c1 E C, and cz E C2} E = {c ® c2 : G € C, and cz E C2}. Show that these are also block linear codes and study their properties in terms of those of the original codes. Show in particular that dp = min {2d1, d2}