Question: Show that if there exists a binary ( n , M , d ) - code, then there exists a binary ( n 1 ,

Show that if there exists a binary (n, M,d)-code, then
there exists a binary (n 1, M, d)-code with M=M/2.
Deduce that A,(n, d)<2A,(n 1, d

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Programming Questions!

Q:

4. (a) Let C be a binary (n, M, d) code, let C" be the binary repetition code of length n, and let C" be the binary code obtained by applying the Plotkin construction to the pair (C, C'). If 2d

Q:

If there is a binary (n, M, d) code, show that there is a binary (n - 1, M', d' ) code with M' ~ ~ and d' ~ d. [Hint: At least half the words of the (n, M, d) code must start with the same symbol....

Q:

Show that if there exists a binary (n, M. d)-code, then there also exists a binary (n-1, M', d)-code with M' > M/2. Deduce the following: A(n, d) 2A(n-1.d)

Q:

Show that if there is a binary ( n , M , d ) - code with d even, then there exists a binary ( n , M , d ) - code in which all the codewords have even weight.

Q:

Recall that Aq(n, d) denotes the largest value of M such that there exists an (n, M, d)- code over a q-ary alphabet. (a) Show that A,(n, d) q-d+1. (The Singleton bound). (b) Use (a) to show that, for...

Q:

Three alternative representations for non-negative integers, n, are: Peano: values have the form S(... S(Z) ...), applying S n times to Z where S and Z are constructors or constants of some data...

Q:

What is an operating system kernel, and what runtime services does an executable binary program expect from a typical time-sharing kernel? How may transfer of control (program flow) between the...

Q:

Story plot: tall, square, symmetric. For each technique, give the relevant matrix equations to obtain the solution x, and point out the properties of the matrices involved. Highlight one potential...

Q:

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Q:

rr1 all questions should be answered correctly SECTION C 9 Foundations of Functional Programming Consider binary trees that are either empty (written Lf) or have the form Br x t1 t2 where t1 and t2...

Q:

A steel with the BCC crystal structure containing 0.001% N is nitrided at 550 C for 5 h. If the nitrogen content at the steel surface is 0.08%, determine the nitrogen content at 0.25 mm from the...

Q:

Actual carry trade profits that are based on actual expected depreciation indicate that: uncovered interest parity does not hold systematically, and on average the carry trade is profitable....

Q:

In case of a bank guarantee, what document is issued by a bank, under which payment is made to the importer on demand upon failure of the eq Letter of credit Standby letter of credit Letter of...

Q:

A robot begins at point C and travels in a straight line across a warehouse oor to point A where it picks up some merchandise. It then turns a 360 corner and travels 50.3 m to point B where it drops...