A memory system according to the embodiment comprises a cell array of plural cells having three or more settable physical quantity levels and operative to store a code composed of symbols expressed by elements in a finite field Zp (p is a prime), wherein a set of two cells is defined as a pair cell and a combination of physical quantity levels of the two cells contained in the pair cell is defined as a pair cell level, wherein the pair cell uses a pair cell level of plural pair cell levels, which maximizes or minimizes a physical quantity level of one cell contained in the pair cell, to assign elements in the Zp to the pair cell levels, thereby storing symbols of the code.
1. A memory system, comprising:
a cell array of plural cells having three or more settable physical quantity levels and operative to store a code composed of symbols expressed by elements in a finite field Zp (p is a prime),
wherein a set of two cells is defined as a pair cell and a combination of physical quantity levels of said two cells contained in said pair cell is defined as a pair cell level,
wherein said pair cell uses a pair cell level of plural pair cell levels, which maximizes or minimizes a physical quantity level of one cell contained in said pair cell, to assign elements in said Zp to said pair cell levels, thereby storing symbols of said code.
2. The memory system according to claim 1 , wherein said pair cell assigns said pair cell levels to elements in said Zp so that a variation of one level in physical quantity level of one cell contained in said pair cell causes a variation within one in element in said Zp.
3. The memory system according to claim 1 , wherein said pair cell assigns part of elements in said Zp to plural levels of said pair cell levels.
4. The memory system according to claim 1 , wherein said pair cell assigns said pair cell levels to elements in said Zp where p=11 when physical quantity levels of said cells contained in said pair cell are 4 levels.
5. The memory system according to claim 1 , wherein said pair cell assigns said pair cell levels to elements in said Zp where p=13 when physical quantity levels of said cells contained in said pair cell are 5 levels.
6. The memory system according to claim 1 , wherein said pair cell assigns said pair cell levels to elements in said Zp where p=17 or 19 when physical quantity levels of said cells contained in said pair cell are 6 levels.
7. The memory system according to claim 1 , wherein said code stored in said cell array is a Lee metric code composed of symbols expressed by elements in said Zp.
8. The memory system according to claim 1 , wherein said plural cells each include a variable resistance element having a structure of nanotubes stacked.