The Divisor In A Cyclic Code Is Normally Called The

The Divisor In A Cyclic Code Is Normally Called The 3,6/5 5205 votes

LCD Cyclic Codes over Finite Fields Chengju Li, Cunsheng Ding, and Shuxing Li Abstract In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes – a class of linear codes – have been employed in cryptog raphy recently. LCD cyclic codes were referred to as reversible cyclic codes in the. On the Construction of Skew Quasi-Cyclic Codes† Taher Abualrub, Ali Ghrayeb, Nuh Aydin, and Irfan Siap Abstract In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings Fx;θ.

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FILL IN THE BLANKS:
1 Which error detection method uses one's complement arithmetic?
A) Simple parity check
B) Two-dimensional parity check
C) CRC
D) Checksum
2 Which error detection method consists of just one redundant bit per data unit?
A) Simple parity check
B) Two-dimensional parity check
C) CRC
D) Checksum
3 In cyclic redundancy checking, what is the CRC?
A) The divisor
B) The quotient
C) The dividend
D) The remainder
4 In cyclic redundancy checking, the divisor is _______ the CRC.
A) The same size as
B) one bit less than
C) one bit more than
D) none of the above
5 A burst error means that two or more bits in the data unit have changed.
A) double-bit
B) burst
C) single-bit
D) none of the above
6 In ________ error correction, the receiver corrects errors without requesting retransmission.
A) backward
B) onward
C) forward
D) none of the above
7 In ________ error correction, the receiver asks the sender to send the data again.
A) backward
B) retransmission
C) forward
D) none of the above
8 We can divide coding schemes into two broad categories: ________ and ______coding.
A) block; linear
B) linear; nonlinear
.
C) block; convolution
D) none of the above
9 In modulo-2 arithmetic, __________ give the same results.
A) addition and multiplication
B) addition and division
C) addition and subtraction
D) none of the above
10 In modulo-2 arithmetic, we use the ______ operation for both addition and subtraction.
This is the correct answer.
A) XOR
B) OR
C) AND
D) none of the above
11 In _____ coding, we divide our message into blocks, each of k bits, called ___.
A) block; blockwords
B) linear; datawords
C) block; datawords
D) none of the above
12 We add r redundant bits to each block to make the length n = k + r. The resulting n-bit blocks are called _________.
A) datawords
B) blockwords
C) codewords
D) none of the above
13 The ________ between two words is the number of differences between corresponding bits.
A) Hamming code
B) Hamming distance
C) Hamming rule
D) none of the above
14 To guarantee the detection of up to 5 errors in all cases, the minimum Hamming distance in a block code must be _______.
A) 5
B) 6
C) 11
D) none of the above
15 To guarantee correction of up to 5 errors in all cases, the minimum Hamming distance in a block code must be ________.
A) 5
B) 6
C) 11
D) none of the above
16 In a linear block code, the _______ of any two valid codewords creates another valid codeword.
A) XORing
B) ORing
C) ANDing
D) none of the above
17 A simple parity-check code can detect __________ errors.
A) an even-number of
B) two
C) no errors
D) an odd-number of

18 _______codes are special linear block codes with one extra property. If a codeword is rotated, the result is another codeword.
A) Non-linear
B) Convolution
C) Cyclic
D) none of the above
19 The _____of errors is more difficult than the ______.
A) correction; detection
B) detection; correction
C) creation; correction
D) creation; detection
20 In modulo-11 arithmetic, we use only the integers in the range ______, inclusive.
A) 1 to 10
B) 1 to 11
C) 0 to 10
D) none of the above
21 In modulo-2 arithmetic, we use only ______.
A) 1 and 2
B) 0 and 2
C) 0 and 1
D) none of the above
22 Adding 1 and 1 in modulo-2 arithmetic results in _________.
A) 1
B) 2
C) 0
D) none of the above
23 In block coding, if k =2 and n =3, we have _______ invalid codewords.
A) 8
B) 4
C) 2
D) none of the above
24 The Hamming distance between equal codewords is _________.
A) 1
B) n
C) 0
D) none of the above
25 The Hamming distance between 100 and 001 is ________.
A) 2
B) 0
C) 1
D) none of the above
26 In block coding, if n = 5, the maximum Hamming distance between two codewords is ________.
A) 2
B) 3
C) 5
D) none of the above
27 If the Hamming distance between a dataword and the corresponding codeword is three, there are _____ bits in error.
A) 3
B) 4
C) 5
D) none of the above
28 The _______ of a polynomial is the highest power in the polynomial.
A) range
.
B) degree
C) power
D) none of the above
29 The divisor in a cyclic code is normally called the _________.
A) degree
B) generator
C) redundancy
D) none of the above
30 A generator that contains a factor of ____ can detect all odd-numbered errors.
A) x
B) x + 1
C) 1
D) none of the above
31 Checksums use _________ arithmetic.
A) two's complement arithmetic
B) one's complement arithmetic
C) either (a) or (b)
D) none of the above
32 In one's complement arithmetic, if positive 7 is 0111, then negative 7 is ________.
A) 1111
B) 1101
C) 1000
D) none of the above
33 The checksum of 1111 and 1111 is _________.
A) 1111
B) 0000
C) 1110
D) 0111
34 The checksum of 0000 and 0000 is __________.
A) 1111
B) 0000
C) 1110
D) 0111
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In-Depth Information
It can be seen that the polynomial representation can easily simplify the operation
of division in this case, because the two steps involving all-0s divisors are not needed
here. (Of course, one could argue that the all-0s divisor step can also be eliminated in
binary division.) In a polynomial representation, the divisor is normally referred to as
The divisor in a cyclic code is normally called the generator polynomial
We can analyze a cyclic code to find its capabilities by using polynomials. We define
the following, where f(x) is a polynomial with binary coefficients.
Redundancy
If s(x)is not zero, then one or more bits is corrupted. However, if s(x) is zero, either
no bit is corrupted or the decoder failed to detect any errors. (Note that ¦ means divide).
1. If s (x) ¦ 0, one or more bits is corrupted.
a. No bit is corrupted, or
b. Some bits are corrupted, but the decoder failed to detect them.
In our analysis we want to find the criteria that must be imposed on the generator,
g (x) to detect the type of error we especially want to be detected. Let us first find the
relationship among the sent codeword, error, received codeword, and the generator.
In other words, the received codeword is the sum of the sent codeword and the
error. The receiver divides the received codeword by g (x) to get the syndrome. We can
g()
g()
g()
The first term at the right-hand side of the equality has a remainder of zero
(according to the definition of codeword). So the syndrome is actually the remainder of
the second term on the right-hand side. If this term does not have a remainder (syn-
0), either e(x) is 0 or e(x) is divisible by g (x). We do not have to worry about
the first case (there is no error); the second case is very important. Those errors that are
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The Divisor In A Cyclic Code Is Normally Called The
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