HW8_solns

# HW8_solns - MATH 3360 Solutions for Selected Porblems in...

This preview shows pages 1–2. Sign up to view the full content.

MATH 3360 Solutions for Selected Porblems in Assignment 8 CS 2.12 One can use the sphere-packing bound equation to see if the code is perfect. However, a more intuitive way is this: | C | = 9, d ( C ) = 3 (Check!), and umber of possible words = 81. Since d ( C ) = 2(1)+1, the sphere has radius 1. Therefore, if c = ( a 1 ,a 2 ,a 3 ,a 4 ) C , the sphere containing c contains the words { c, ( a 1 ± 1 ,a 2 ,a 3 ,a 4 ) , ( a 1 ,a 2 ± 1 ,a 3 ,a 4 ) , ( a 1 ,a 2 ,a 3 ± 1 ,a 4 ) , ( a 1 ,a 2 ,a 3 ,a 4 ± 1) } which has 9 elements. So the 9 spheres corresponding to the 9 codes covers 9 × 9 = 81 elements, i.e. the code is perfect. CS 2.19 Note that we want 3 linear dependent columns in the parity check matrix H . No two columns are linearly dependent since (ONLY) in binary code, two vectors are linearly depdendent iﬀ they are equal or one or more of them are zero vectors. 13B 6 i) g ( x ) is a unit is not equivalent to g (1) ,g (2) ,g (3) ,g (0) 6 = 0 , 2. ii) One can easily check (1+2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/05/2011 for the course MATH 3360 taught by Professor Billera during the Spring '08 term at Cornell.

### Page1 / 2

HW8_solns - MATH 3360 Solutions for Selected Porblems in...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online