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added field_based and used it whenever needed
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@dimpase
dimpase committed May 12, 2017
1 parent 5d2ee22 commit e793a92
Showing 1 changed file with 39 additions and 74 deletions.
113 changes: 39 additions & 74 deletions src/sage/coding/code_bounds.py
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Expand Up @@ -177,26 +177,42 @@
from .delsarte_bounds import delsarte_bound_hamming_space, \
delsarte_bound_additive_hamming_space

def _check_n_q_d(n, q, d):
def _check_n_q_d(n, q, d, field_based=True):
r"""
Check that the length `n`, alphabet size `q` and minimum distance `d` type
check and make sense for a code over a field.
More precisely, checks that the parameters are positive integers, that `q`
is a prime power, and that `n >= d`. Raises a ``ValueError`` otherwise.
is a prime power for codes over a field, or, more generally, that
`q` is of size at least 2, and that `n >= d`. Raises a ``ValueError``
otherwise.
EXAMPLES::
TESTS::
sage: from sage.coding.code_bounds import _check_n_q_d
sage: _check_n_q_d(20, 16, 5)
True
sage: _check_n_q_d(20, 16, 21)
sage: _check_n_q_d(20, 16, 6, field_based=False)
True
sage: _check_n_q_d(20, 21, 16)
Traceback (most recent call last):
...
ValueError: The alphabet size does not make sense for a code over a field
sage: _check_n_q_d(20, -21, 16)
Traceback (most recent call last):
...
ValueError: The alphabet size must be an integer >1
sage: _check_n_q_d(20, 2, 26)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
ValueError: The length or minimum distance does not make sense
"""
if not( is_prime_power(q) and d > 0 and n >= d and n in ZZ and d in ZZ ):
raise ValueError("The length, alphabet size and minimum distance does not make sense for a code over a field")
if (q not in ZZ) or (q<2):
raise ValueError("The alphabet size must be an integer >1")
if field_based==True and (not is_prime_power(q)):
raise ValueError("The alphabet size does not make sense for a code over a field")
if not( d > 0 and n >= d and n in ZZ and d in ZZ ):
raise ValueError("The length or minimum distance does not make sense")
return True


Expand Down Expand Up @@ -248,12 +264,13 @@ def codesize_upper_bound(n,d,q,algorithm=None):
20
Meaningless parameters are rejected::
sage: codes.bounds.codesize_upper_bound(10, 20, 16)
sage: codes.bounds.codesize_upper_bound(10, -20, 6)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
ValueError: The length or minimum distance does not make sense
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
if algorithm=="gap":
gap.load_package('guava')
return int(gap.eval("UpperBound(%s,%s,%s)"%( n, d, q )))
Expand Down Expand Up @@ -288,11 +305,10 @@ def dimension_upper_bound(n,d,q,algorithm=None):
Meaningless code parameters are rejected::
sage: codes.bounds.dimension_upper_bound(-3,3,2)
sage: codes.bounds.dimension_upper_bound(13,3,6)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
ValueError: The alphabet size does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
q = ZZ(q)
Expand Down Expand Up @@ -328,17 +344,8 @@ def gilbert_lower_bound(n,q,d):
sage: codes.bounds.gilbert_lower_bound(10,2,3)
128/7
TESTS:
Meaningless parameters are rejected::
sage: codes.bounds.gilbert_lower_bound(10, 6, 3)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
ans=q**n/volume_hamming(n,q,d-1)
return ans

Expand All @@ -359,17 +366,8 @@ def plotkin_upper_bound(n,q,d, algorithm=None):
192
sage: codes.bounds.plotkin_upper_bound(10,2,3,algorithm="gap") # optional - gap_packages (Guava package)
192
TESTS:
Meaningless parameters are rejected::
sage: codes.bounds.plotkin_upper_bound(10, 16, 20)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
if algorithm=="gap":
gap.load_package("guava")
ans=gap.eval("UpperBoundPlotkin(%s,%s,%s)"%(n,d,q))
Expand Down Expand Up @@ -425,13 +423,6 @@ def griesmer_upper_bound(n,q,d,algorithm=None):
243
sage: codes.bounds.griesmer_upper_bound(11,3,6)
243
Meaningless parameters are rejected::
sage: codes.bounds.griesmer_upper_bound(10, 16, 20)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
if algorithm=="gap":
Expand Down Expand Up @@ -466,17 +457,8 @@ def elias_upper_bound(n,q,d,algorithm=None):
232
sage: codes.bounds.elias_upper_bound(10,2,3,algorithm="gap") # optional - gap_packages (Guava package)
232
TESTS:
Meaningless parameters are rejected::
sage: codes.bounds.elias_upper_bound(10, 16, 20)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
r = 1-1/q
if algorithm=="gap":
gap.load_package("guava")
Expand All @@ -500,13 +482,14 @@ def hamming_upper_bound(n,q,d):
Returns the Hamming upper bound.
Returns the Hamming upper bound for number of elements in the
largest code of minimum distance d in `\GF{q}^n`.
largest code of length n and minimum distance d over alphabet
of size q.
The Hamming bound (also known as the sphere packing bound) returns
an upper bound on the size of a code of length `n`, minimum distance
`d`, over a field of size `q`. The Hamming bound is obtained by
dividing the contents of the entire space
`\GF{q}^n` by the contents of a ball with radius
`d`, over an alphabet of size `q`. The Hamming bound is obtained by
dividing the contents of the entire Hamming space
`q^n` by the contents of a ball with radius
`floor((d-1)/2)`. As all these balls are disjoint, they can never
contain more than the whole vector space.
Expand All @@ -526,17 +509,8 @@ def hamming_upper_bound(n,q,d):
sage: codes.bounds.hamming_upper_bound(10,2,3)
93
TESTS:
Meaningless parameters are rejected::
sage: codes.bounds.hamming_upper_bound(10, 16, 20)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
return int((q**n)/(volume_hamming(n, q, int((d-1)/2))))

def singleton_upper_bound(n,q,d):
Expand All @@ -563,17 +537,8 @@ def singleton_upper_bound(n,q,d):
sage: codes.bounds.singleton_upper_bound(10,2,3)
256
TESTS:
Meaningless parameters are rejected::
sage: codes.bounds.singleton_upper_bound(10, 16, 20)
Traceback (most recent call last):
...
ValueError: The length, alphabet size and minimum distance does not make sense for a code over a field
"""
_check_n_q_d(n, q, d)
_check_n_q_d(n, q, d, field_based=False)
return q**(n - d + 1)

def gv_info_rate(n,delta,q):
Expand Down

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