1

# Let C be linear binary code of length n . For i ﾃ｢窶堋ｬ {1,2, ~n} let e(i) be the word with 1 in position i and 0 in all other positions. Suppose that H is a parity...

## Question

###### Let C be linear binary code of length n . For i ﾃ｢窶堋ｬ {1,2, ~n} let e(i) be the word with 1 in position i and 0 in all other positions. Suppose that H is a parity check matrix for C. Let v, v ﾃ｢窶堋ｬ Zz. Theorem 14.6 says that C +v = C+v (that is, v and are in the same cosets) if and only if vHtr = U Htr Show that C is one-error correcting if and only if the columns of H are distinct and non-zero.

Let C be linear binary code of length n . For i ﾃ｢窶堋ｬ {1,2, ~n} let e(i) be the word with 1 in position i and 0 in all other positions. Suppose that H is a parity check matrix for C. Let v, v ﾃ｢窶堋ｬ Zz. Theorem 14.6 says that C +v = C+v (that is, v and are in the same cosets) if and only if vHtr = U Htr Show that C is one-error correcting if and only if the columns of H are distinct and non-zero.  #### Similar Solved Questions

##### Question 3 (1 point)Determine whether the series 1 + + 3+4+_+4+_=Y; converges or diverges. 2 3Use the Integral Test;Diverges but Integral Test cannot be usedConverges but Integral Test cannot be usedConverges by Integral TestDiverges by Integral Test
Question 3 (1 point) Determine whether the series 1 + + 3+4+_+4+_=Y; converges or diverges. 2 3 Use the Integral Test; Diverges but Integral Test cannot be used Converges but Integral Test cannot be used Converges by Integral Test Diverges by Integral Test...
##### Er4In Thlinm hrh shom.46"of lglut HicArut neeliun * Ih Inuet enlncilu una Anen Inl IiruaIe TuanMrtuutlar hrlncen Alt and . reutuctt nlo nten Inla, nID Wnich MEcit (uir icdimnMnd 'light thc least? me-dinntal meuium mnuseihlTdtcrummwhich medium the speed of light the greatest? mediuma mUlunI) mcdmit Iminesihlcdetermine)Which medium has the highest index of refraction? nadnnta medhuma mle dnunl umnanetinledelcrmintWhich medium has the lowest index of refraction? mediumi mediumz mediunin i
Er4In Thlinm hrh shom.46"of lglut HicArut neeliun * Ih Inuet enlncilu una Anen Inl IiruaIe TuanMr tuutlar hrlncen Alt and . reutuctt nlo nten Inla, n ID Wnich MEcit (uir icdimn Mnd 'light thc least? me-dinntal meuium mnuseihl Tdtcrumm which medium the speed of light the greatest? mediuma m...
##### #I tore [ 013074 ede"denlan o BODItuecho 7a Lum DanHn_ar Or Jaleicdezn
#I tore [ 013074 ede"denlan o BODItuecho 7a Lum Dan Hn_ar Or Jaleicdezn...
##### When the Hg" + concentration is 1.72 x 10 M, the observed cell potential at 298 K for an electrochemical cell with the following reaction is 1.921 V: What is the Mn concentration?Hg2+ (aq) + Mn(s) + Hg(l) + Mn2+ (aq)IMn? !
When the Hg" + concentration is 1.72 x 10 M, the observed cell potential at 298 K for an electrochemical cell with the following reaction is 1.921 V: What is the Mn concentration? Hg2+ (aq) + Mn(s) + Hg(l) + Mn2+ (aq) IMn? !...
##### Which structure below is not correctly drawn?CH,CH;CCH;CHzCH,CH,NHzOHCH,
Which structure below is not correctly drawn? CH,CH;C CH;CHz CH,CH, NHz OH CH,...
##### 3 ^each Suppose 1 32 Show Sthat ud andes 3 1 transtormation that Rm N 5 W any Iin transformation - 3 3 862Lot Flnd T(u) and 3 and tho then sketch Uanylonnation VL vecton 3 3 1 @F 3 Let #= 76 1
3 ^ each Suppose 1 32 Show Sthat ud andes 3 1 transtormation that Rm N 5 W any Iin transformation - 3 3 862 Lot Flnd T(u) and 3 and tho then sketch Uanylonnation VL vecton 3 3 1 @F 3 Let #= 76 1...
##### Kirby-Bauer Test Timelapse with E. coli and S aureus
Kirby-Bauer Test Timelapse with E. coli and S aureus...
##### [=80 Potmts]DETAILSOSPREcALCI 5.3.223.I}sec(t) 3,87 what is the exact value of sec(~t)?eclamional Diaberial0Book[-/1 Polnts]DETAILSOSPRECALC1 5.3.228_Use the angle in the unit circle to find the exact value of each of the six tngonometnc functions
[=80 Potmts] DETAILS OSPREcALCI 5.3.223. I}sec(t) 3,87 what is the exact value of sec(~t)? eclamional Diaberial 0Book [-/1 Polnts] DETAILS OSPRECALC1 5.3.228_ Use the angle in the unit circle to find the exact value of each of the six tngonometnc functions...
##### Could a telescope with an objective lens of diameter $20 \mathrm{cm}$ resolve two objects a distance of $10 \mathrm{km}$ away separated by $1 \mathrm{cm}$ ? (Assume we are using a wavelength of 600 nm.)
Could a telescope with an objective lens of diameter $20 \mathrm{cm}$ resolve two objects a distance of $10 \mathrm{km}$ away separated by $1 \mathrm{cm}$ ? (Assume we are using a wavelength of 600 nm.)...
##### Quection 24NeWhat (s the most commonly cited mode of macroevolution?GdualismPunctuated cquilibriumAnjkenesisChdorenesls
Quection 24 Ne What (s the most commonly cited mode of macroevolution? Gdualism Punctuated cquilibrium Anjkenesis Chdorenesls...
##### Proof (epsilon-delta definition)
proof (epsilon-delta definition)...
##### Delermine the rise, run; and slope of the line fored by these pointstiseWhat is the enthalpy of vaporization of this liquid?JlmolslopeBH p
Delermine the rise, run; and slope of the line fored by these points tise What is the enthalpy of vaporization of this liquid? Jlmol slope BH p...
##### Incorrect .(62 Use the formula from part (a) to predict the amount of municipal solid waste generated In the US, tons In the year 2022. in milllons of Round vour answer to one decimal place:The model predicts that in the year 2022, tne solid waste generated by cities in the US wlll be milllons of tons: the tolerance Is +/-8%
Incorrect . (62 Use the formula from part (a) to predict the amount of municipal solid waste generated In the US, tons In the year 2022. in milllons of Round vour answer to one decimal place: The model predicts that in the year 2022, tne solid waste generated by cities in the US wlll be milllons of ...
##### How would you "remove the discontinuity" of $f$? In other words, how would you define $f(2)$ in order to make $f$ continuous at 2? $f(x) = \dfrac {x^2 - x - 2}{x - 2}$
How would you "remove the discontinuity" of $f$? In other words, how would you define $f(2)$ in order to make $f$ continuous at 2? $f(x) = \dfrac {x^2 - x - 2}{x - 2}$...
##### Ooslion ennantFind the cibcal VivsIorm 3 confidence Inierval at ita leval 0l conliderxa slxin boli, nacersary0 93(Roura Io ccinul blcatAnd
Ooslion ennant Find the cibcal Vivs Iorm 3 confidence Inierval at ita leval 0l conliderxa slxin boli, nacersary 0 93 (Roura Io ccinul blcat And...