Question

In: Advanced Math

How many cyclic codes of length 4 are there over F5? Find a generator matrix and...

How many cyclic codes of length 4 are there over F5? Find a generator matrix and a parity check matrix for each 2-dimensional code.

Solutions

Expert Solution


Related Solutions

A (7, 4) cyclic code is designed with a generator polynomial, g(D) = D3 + D...
A (7, 4) cyclic code is designed with a generator polynomial, g(D) = D3 + D + 1. a) (10 points) Determine the code word for the message, 1010. b) (10 points) Determine the code word for the message, 1100. c) (9+1= 10 points) Determine the error polynomial for the received word, 1110101. Is the received word correct?
A (7, 4) cyclic code is designed with a generator polynomial, g(D) = D3 + D...
A (7, 4) cyclic code is designed with a generator polynomial, g(D) = D3 + D + 1. a) (10 points) Determine the code word for the message, 1010. b) (10 points) Determine the code word for the message, 1100. c) (9+1= 10 points) Determine the error polynomial for the received word, 1110101. Is the received word correct?
A (7, 4) error correcting Hamming code is designed with a generator matrix, G = ...
A (7, 4) error correcting Hamming code is designed with a generator matrix, G =   1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1   . (1) a) (10 points) Determine the code word for the message, 0110. b) (10 points) Determine the code word for the message, 1100. c) (9 points) Determine the syndrome vector for the...
How many of the 6^4=1296 secret codes in the game of Mastermind (6 colors, 4 positions)...
How many of the 6^4=1296 secret codes in the game of Mastermind (6 colors, 4 positions) use: a.) 4 different colors b.) 2 of one color and 2 of another c.) 2 of one color and 1 each of two other colors
Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ]...
Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ] [ 1 1 6 ] It is a 3*3 matrix
An n-bit binary string is a sequence of length n over the alphabet {0,1}. How many...
An n-bit binary string is a sequence of length n over the alphabet {0,1}. How many n-bit binary strings are there? How many n-bit binary strings b1,…,bn are there such that b1b2≠00? In other words, how many n-bit binary strings don't begin with 00? How many n-bit binary strings b1,…,bn are there such that b1b2≠00 and b2b3≠11? How many n-bit binary strings b1,…,bn are there such that b1b2≠00 and such that b2b3≠01?
Let S be the set of all codes over Fq of length n.LetC1, C2∈ S.DefineC1∼C2to mean...
Let S be the set of all codes over Fq of length n.LetC1, C2∈ S.DefineC1∼C2to mean that there exists an n×n monomial matrix M such that C1=M C2.Probe that∼is an equivalence relation on S.LetC1, C2such that C1∼C2. Do C1 and C2have the same dimension?,length?, minimum distance?, if C1is self-orthogonal, is also C1 self-orthogonal?.
(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4...
(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4 onto the plane P= span 1 -1 -1 1 -1 -1 1 1 (b) Find the distance of vector ~y = 2 0 0 4 from the plane P.
How many electrons in the cyclic and fully conjugated system? Is it aromatic? anti aromatic? Non...
How many electrons in the cyclic and fully conjugated system? Is it aromatic? anti aromatic? Non aromatic?
How to convert wave function to matrix in H2 and LiH . And how to find...
How to convert wave function to matrix in H2 and LiH . And how to find the determinant(energy)?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT