1. (Currently Amended) An encoder which encodes a current block to be encoded in an image,
`
`AMENDMENTS TO THE CLAIMS
`
`the encoder comprising:
`
`circuitry; and
`
`memory,
`
`wherein using the memory,the circuitry:
`
`performs a primary transform on the current block from residuals of the current
`
`block to primary coefficients;
`
`determines whether a secondary transform is to be applied to the current block;
`
`(i) when the secondary transform is not to be applied, calculates quantized
`
`primary coefficients by performinga first quantization on the primary coefficients usinga
`
`quantization matrix, the quantization matrix including quantization steps by which the
`
`respective primary coefficients are divided, andwhen+thesecondarytransfermis-nettebe
`
`appled, (ii) when the secondary transform is to be applied, performs a secondary
`
`transform from the primary coefficients to secondary coefficients, and calculates
`
`quantized secondary coefficients by performing a second quantization on the secondary
`
`coefficients, the second quantization using a quantization step by which eachofthe
`
`secondary coefficients is divided, the quantization step being common between the
`
`
`
`secondary coefficients, and-vhenthe-secondarytransfermistebeappliedthesecond
`
`cation
`
`beine
`
`different
`
`froma
`
`the
`
`&
`
`zation-and
`
`generates an encodedbitstream by encoding either the quantized primary
`
`coefficients or the quantized secondary coefficients.
`
`2. (Original) The encoder according to claim 1,
`
`wherein the first quantization is a weighted quantization using a first quantization matrix,
`
`and
`
`the second quantization is a weighted quantization using a second quantization matrix
`
`different from the first quantization matrix.
`
`3. (Original) The encoder according to claim 2,
`
`
`
`AMENDMENTS TO THE CLAIMS
`
`the encoder comprising:
`
`circuitry; and
`
`memory,
`
`wherein using the memory,the circuitry:
`
`performs a primary transform on the current block from residuals of the current
`
`block to primary coefficients;
`
`determines whether a secondary transform is to be applied to the current block;
`
`(i) when the secondary transform is not to be applied, calculates quantized
`
`primary coefficients by performinga first quantization on the primary coefficients usinga
`
`quantization matrix, the quantization matrix including quantization steps by which the
`
`respective primary coefficients are divided, andwhen+thesecondarytransfermis-nettebe
`
`appled, (ii) when the secondary transform is to be applied, performs a secondary
`
`transform from the primary coefficients to secondary coefficients, and calculates
`
`quantized secondary coefficients by performing a second quantization on the secondary
`
`coefficients, the second quantization using a quantization step by which eachofthe
`
`secondary coefficients is divided, the quantization step being common between the
`
`
`
`secondary coefficients, and-vhenthe-secondarytransfermistebeappliedthesecond
`
`cation
`
`beine
`
`different
`
`froma
`
`the
`
`&
`
`zation-and
`
`generates an encodedbitstream by encoding either the quantized primary
`
`coefficients or the quantized secondary coefficients.
`
`2. (Original) The encoder according to claim 1,
`
`wherein the first quantization is a weighted quantization using a first quantization matrix,
`
`and
`
`the second quantization is a weighted quantization using a second quantization matrix
`
`different from the first quantization matrix.
`
`3. (Original) The encoder according to claim 2,
`
`
`
`wherein the circuitry writes the first quantization matrix and the second quantization
`
`matrix into the encoded bitstream.
`
`4. (Original) The encoder according to claim 3,
`
`wherein the primary coefficients include one or morefirst primary coefficients and one or
`
`more second primary coefficients,
`
`the secondary transform is applied to the one or morefirst primary coefficients and is not
`
`applied to the one or more second primary coefficients,
`
`the second quantization matrix has one or more first componentvalues corresponding to
`
`the one or morefirst primary coefficients and one or more second component values
`
`corresponding to the one or more second primary coefficients,
`
`each of the one or more second componentvalues of the second quantization matrix
`
`matches a corresponding one of componentvaluesofthe first quantization matrix, and
`
`whenthe circuitry writes the second quantization matrix, the circuitry writes, into the
`
`encodedbitstream, only the one or more first component values among the one or morefirst
`
`component values and the one or more second componentvalues.
`
`5. (Original) The encoder accordingto claim 3,
`
`wherein in the secondary transform, a plurality of bases which has been determined is
`
`selectively used,
`
`the encoded bitstream includes a plurality of second quantization matrices corresponding
`
`to the plurality of bases, and
`
`in the second quantization, a second quantization matrix corresponding to a basis used for
`
`the second transform is selected from the plurality of second quantization matrices.
`
`6. (Original) The encoder according to claim 2,
`
`wherein the first quantization matrix and the second quantization matrix are defined in
`
`advance in a standard.
`
`7. (Original) The encoder according to claim 2,
`
`
`
`wherein the circuitry derives the second quantization matrix from the first quantization
`
`matrix.
`
`8. (Original) The encoder accordingto claim 7,
`
`wherein the primary coefficients include one or morefirst primary coefficients and one or
`
`more second primary coefficients,
`
`the secondary transform is applied to the one or morefirst primary coefficients and is not
`
`applied to the one or more second primary coefficients,
`
`the second quantization matrix has one or more first component values corresponding to
`
`the one or morefirst primary coefficients and one or more second component values
`
`corresponding to the one or more second primary coefficients,
`
`each of the one or more second component values of the second quantization matrix
`
`matches a corresponding one of componentvaluesofthe first quantization matrix, and
`
`whenthecircuitry derives the second quantization matrix, the circuitry derives the one or
`
`more first componentvalues of the second quantization matrix from the first quantization matrix.
`
`9. (Original) The encoder according to claim 7,
`
`wherein the second quantization matrix is derived by applying the secondary transform to
`
`the first quantization matrix.
`
`10. (Original) The encoder accordingto claim 7,
`
`wherein the circuitry:
`
`derives a third quantization matrix from the first quantization matrix, the third
`
`quantization matrix having component values which are greater when corresponding component
`
`values ofthe first quantization matrix are smaller;
`
`derives a fourth quantization matrix by applying the secondary transform to the third
`
`quantization matrix; and
`
`derives, as the second quantization matrix, a fifth quantization matrix from the fourth
`
`quantization matrix, the fifth quantization matrix having component values which are greater
`
`when corresponding componentvalues of the fourth quantization matrix are smaller.
`
`
`
`11. (Original) The encoder according to claim 10,
`
`wherein the componentvalues of the third quantization matrix are reciprocals of the
`
`corresponding componentvaluesofthe first quantization matrix, and
`
`the componentvalues ofthe fifth quantization matrix are reciprocals of the corresponding
`
`component values of the fourth quantization matrix.
`
`12. (Original) The encoderaccordingto claim 1,
`
`wherein the first quantization is a weighted quantization in which a quantization matrix is
`
`used, and
`
`the second quantization is a non-weighted quantization in which no quantization matrix is
`
`used.
`
`13. (Currently Amended) The encoderaccording to claim 1,
`
`wherein the first quantization is a weighted quantization using a first quantization matrix,
`
`in the secondary transform,(i) weighted primary coefficients are calculated by
`
`multiplying each of the primary coefficients by a corresponding componentvalue of a weighting
`
`matrix, and (ii) the weighted primary coefficients are transformed into secondary coefficients.;
`
`
`
`14. (Original) The encoder according to claim 13,
`
`wherein the circuitry derives the weighting matrix from thefirst quantization matrix.
`
`15. (Currently Amended) The encoderaccording to claim L.elatn43,
`
`wherein the circuitry derives the common quantization step from a quantization
`
`parameter for the current block.
`
`16. (Currently Amended) An encoding method for encoding a current block to be encoded in an
`
`image, the encoding method comprising:
`
`
`
`performing a primary transform from residuals of the current block to primary
`
`coefficients;
`
`determining whether a secondary transform is to be applied to the current block;
`
`(i) when the secondary transform is not to be applied, calculating quantized primary
`
`coefficients by performing a first quantization on the primary coefficients using a quantization
`
`matrix, the quantization matrix including quantization steps by which the respective primary
`
`
`
`
`coefficients are divided, andwhen+the-secondarytransformisnette-be-appled,(11) when the
`
`secondary transform is to be applied, performing a secondary transform from the primary
`
`coefficients to secondary coefficients, and calculating quantized secondary coefficients by
`
`performing a second quantization on the secondary coefficients, the second quantization using a
`
`quantization step by which each of the secondary coefficients is divided, the quantization step
`
`being common between the secondary coefficients; and-vhenthesecondarytransfermistebe
`od
`Oran
`am-the
`oO
`4
`On
`nd
`=
`
`a
`
`?
`
`generating an encodedbitstream by encoding either the quantized primary coefficients or
`
`the quantized secondary coefficients.
`
`17 — 41. (Cancelled)
`
`
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