<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-06-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000202058</issuerCik>
        <issuerName>HARRIS CORP /DE/</issuerName>
        <issuerTradingSymbol>HRS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001191551</rptOwnerCik>
            <rptOwnerName>STOFFEL JAMES C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11 WOODBURY PLACE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROCHESTER</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>14618</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>I</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>153.48</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, Par Value $1.00</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20400</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15.15</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each phantom stock unit is the economic equivalent of one share of the Issuer's common stock.</footnote>
        <footnote id="F2">The phantom stock units were accrued under the Harris Corporation 2005 Directors' Deferred Compensation Plan.  The phantom stock units are to be settled in cash upon the reporting person's retirement or other events.  The reporting person may also transfer the phantom stock units into alternative investment accounts in certain other instances if applicable ownership guidelines are satisfied.</footnote>
    </footnotes>

    <remarks>Exhibit List:

Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>By:  /s/ Scott T. Mikuen, Attorney-in-Fact,
For:  James C. Stoffel</signatureName>
        <signatureDate>2018-06-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
